Please help to advise whether my itinerary makes sense or not

If your plane lands at 6am you have no chance of catching a train from Paddington at 7.45. You need to leave about an hour to through immigration and collect your bags and then another hour to get to Paddington station and leave some contingency for if anything goes wrong.

Another alternative is to take a National Express bus straight from Heathrow to Bath - that might be just as quick and less hassle depending on the timetable.

Why don't you take a train from Bath straight to York. You will have to change in Bristol but it's more convenient than going all the way back to London, spending an overnight there and leaving early the next morning.

Overall it seems incredibly rushed seeing 5 cities in what seems like just a few days. It would make more sense to have an open-jaw flight flying into London and out from either Edinburgh or Brussels, but maybe that's already booked?

Couple ideas. Maybe add your 2 days in Bath to the 4 days in London at the end? It would save time and $ to fly from Edinburgh to Paris or Brussels.

If you leave Edinburgh at 2.30pm it is not possible to catch the 6.30 or 7.30 Eurostar as you have a 75 minute check in at St Pancras. You also need to allow a buffer as well in case of any train delays.
On a purely statistical basis, on a 393 mile journey I would expect to be about 43 minutes late. Chances are you will be close to time, but that is the mean delay.

On Day 1 you have no idea what time you will actually land. That means you can't book any kind of discount train fare, so will pay peak time high fares before 9.30am on weekdays. Well you can book, but it is a huge gamble.
If you were on time there is a flixbus to Bath at 0740, and National Express at 0750. But then multi hour waits to the next one for either company.

The last daytime connection Bath to York is at 2013, arrive 0131. There is also an overnight seated connection at 2113, arrive 0320.

How many nights will you sleep in Europe? Are there cities you want to visit more than others? Have you considered flying in and out of Edinburgh and Paris or Paris and Edinburgh?
Bath is a day trip from London so no need to spend the night in Bath. Ghent, Bruges and Antwerp are day trips from Brussels which makes the logistics easier and takes less time than sleeping in Bruges for example.

If your plane lands at 6am you have no chance of catching a train from
Paddington at 7.45. You need to leave about an hour to through
immigration and collect your bags and then another hour to get to
Paddington station and leave some contingency for if anything goes
wrong.

Ok, is it sufficient to book 8am train to Bath from Paddington station? I think I estimate 30 minutes arrival at Paddington station from Heathrow airport. The Elizabeth line takes around 27-28 minutes for the journey between Heathrow and Paddington. I need to buy some food before boarding the 8am train journey for the Bath. Is it alright?

Why don't you take a train from Bath straight to York. You will have
to change in Bristol but it's more convenient than going all the way
back to London, spending an overnight there and leaving early the next
morning.

You are right! I thought mistakenly that travelling directly from Bath to York via Bristol takes 6 hours. I checked and find that it takes only 4.5 hours. Not bad. Ok, i will take that route. Thanks for your suggestion.

Maybe add your 2 days in Bath to the 4 days in London at the end? It
would save time and $ to fly from Edinburgh to Paris or Brussels.

Fly from Edinburgh to Paris or Brussels? I consider but I prefer to travel on train because i prefer to enjoy sightseeing while on the train journey.

that's before the large problem of needing a 90 minutes checkin
allowance before the departure time. So you need to leave Edinburgh at
least 2 hours earlier.

RS travel book advises that arrive early to go through security and passport control must be completed at least 30 minutes before departure. I arrive at terminal 2 at Heathrow airport.

Ok, i calculate and decide that it would be good to depart from Edinburgh at 1:30pm and arrive at London King Cross at 6pm and then check in at least 45 minutes early before boarding for 7pm journey to depart for Paris. How about that?

Bath is a day trip from London so no need to spend the night in Bath.

No need to spend a night in Bath? Really? Hmm....my trip at Bath is to do sightseeing:
1. Roman Baths
2. Bath Abbey
3. The Circus and Royal Crescent

Is it normal-paced to do sightseeing of these places? Not hurried. Relaxing for one day?

Is it a hassle to store luggage in luggage storage services? I think depart from Bath for York at 6:30pm instead of 6pm. I need to spend a bit more to enjoy Bath. Is it expensive to buy tickets on the spot?

Regarding connecting to Eurostar the RS book is just incorrect. The required check in time is 75 minutes currently.
Even assuming no delay on the train from Edinburgh you have to exit Kings Cross, cross the street, then walk through St Pancras.
You may be very lucky and they may accept you at 45 minutes, and you won't be significantly sooner than that, then process you in 15 minutes, but 75 minutes IS the minimum specified check in time.
If you are not accepted your ticket will be void. You then have to buy a new ticket for the last train at 8pm at some extortionate rate.
Tonight that price is £242.
A very expensive mistake.
If you want to leave Edinburgh at 1.30 you have to book the 8pm Eurostar. If the Edinburgh train is delayed you risk being stranded in London overnight.

If you buy a last minute ticket from Bath to York via Bristol it will cost you £257.20. So buy a last minute Bath to Bristol for £10.20 and Bristol to York for £118.50.

Heathrow to Bath- you are taking a massive gamble on the flight being on time, then clearing Immigration fast at a busy time of the morning. At Paddington you have to transfer from the Elizabeth Line station to the main line station.
Yes you might make it for 8am but your chances are maybe 50:50.
If the flight is on time, and is blown over by the jet stream and you are processed fast you may even get the 7.30 train by fluke luck.
The train to Bath has a food car if you don't have time to go shopping.
Miss your train and it's a new ticket at £129.30.

I seriously think you need to look at buying a Britrail pass if buying last minute tickets like this, and seriously review the Edinburgh to Paris journey.

If you sleep in Bath take a direct bus from London Heathrow airport (terminals one and two) instead of a train from the airport to Paddington station to Bath. The fewer the transfers the easier it is, especially when hauling luggage. Bus travel is easier if you pack heavy because you stow your bags before getting on the bus.

Is it expensive to buy tickets on the spot?

The earlier you buy train tickets the cheaper it is. It also takes time to buy a ticket since lines are long but the ticket machines have shorter lines. Make sure you buy your Eurostar tickets when your itinerary is set and you have already bought your plane tickets and reserved lodging. Eurostar tickets are expensive when you buy them just before leaving home.
Instead of taking a 6p train from Bath to London and spending the night, why not sleep in Bath and the next morning take a train from Bath to York? You will lose a day, but it will be a much more relaxed trip. Are you an early riser?

https://www.eurostar.com/rw-en/travel-info/your-trip/check-in
See the different time for the check-in before departure for different cities at Eurostar.

isn31c, thanks for your advice. I modified my journey a bit.

I decide to depart for Bath on first day evening instead of early morning and stay overnight in London upon my arrival from Edinburgh and spend a whole day on london before depart for Paris evening. Very relaxing.

I read somewhere that staying at Antwerp or Bruges is much nicer than in Brussels. What do you think?

Hmm....my trip at Bath is to do sightseeing for only one day:
1. Roman Baths
2. Bath Abbey
3. The Circus and Royal Crescent

Is one day normal-paced to do sightseeing of these places? Not hurried. Relaxing for one day?

That is a far better paced itinerary now.

If you have the opportunity I would stay in Bruges as long as possible…..we were in Brussels and Bruges in late spring and would definitely choose Bruges over Brussels any day…….just so charming and lovely and easy to navigate.

If you have the opportunity I would stay in Bruges as long as
possible…..we were in Brussels and Bruges in late spring and would
definitely choose Bruges over Brussels any day…….just so charming and
lovely and easy to navigate.

Really tough. Why? From Paris, I arrive at Brussels Midi and do sightseeing in Brussels first before going to Bruges -> Ghent -> Antwerp. Means i have to stay at Brussels for few nights, not Bruges. Brussels is the central stop for Bruges, Ghent and Antwerp. After all that, I have to go back to London via Eurostar from Brussels.

I agree with Jane. I would prefer to come "home" every night to charming Bruges or maybe Ghent than Brussels.

You can easily day trip to Brussels and Antwerp from Bruges or Ghent. Or with an early Brussels arrival, store your luggage at the station and see the city before taking the train to Bruges or Ghent.

And it is an easy transfer to/from the Eurostar in Brussels to local trains.

After doing some research, I think that York and Bath is not easy to navigate to visit the interesting places and accomodations.

Roman Baths and Bath Abbey are quite far away from The Circus and Royal Crescent.

As for York, some interesting places such as York Minister and York Castle Museum are far away from the train station and each other. Gosh. I'm worried that i might not find my way to the accomodations for Bath and York in evening/night.

You can easily day trip to Brussels and Antwerp from Bruges or Ghent.
Or with an early Brussels arrival, store your luggage at the station
and see the city before taking the train to Bruges or Ghent.

And it is an easy transfer to/from the Eurostar in Brussels to local
trains.

Oh well, it is not easy, i think because I might spend 2 days sightseeing in Brussels as there are several interesting places. As for Bruges, Ghent and Antwerp, there are few interesting places per city. Let's imagine, let's say i stay in Bruges for few nights, how to spend my day to see around in Brussels for 2 days without staying in Brussels. Which means i have to take a train to visit Brussels twice. Or i stay in Brussels for 2 nights then stay in Bruges for 2 nights - 1 day to do sightseeing in Bruges and 1 day sightseeing in Ghent and Antwerp and then go back from Bruges to Brussels to London via Eurostar? I think it might be a bit challenging for me if i choose this former way.

Gent is in an excellent location for short trips to Bruges, Brussels, Antwerpen and Mechelen. Great town, centrally located.

Blockquote

After doing some research, I think that York and Bath is not easy to navigate to visit the interesting places and accomodations.

Roman Baths and Bath Abbey are quite far away from The Circus and Royal Crescent.

As for York, some interesting places such as York Minister and York Castle Museum are far away from the train station and each other. Gosh. I'm worried that i might not find my way to the accomodations for Bath and York in evening/night.

Blockquote

Have you looked these places up on Google Maps? . You can walk between any of these places, in each city, in about 15-20 minutes, and the walks are charming. If you are that worried about finding your hotel from the station, just take a taxi. I've been to both places and found the streets well marked and well lit. If you have a phone with data, there's no reason to get lost.

Sorry for not being clear. Actually I wanted to say that i might not be able to find my accomodation in the evening upon my arrival in Bath/York because I might not see well/clearly in the dark compared to the day. I intend to arrive in Bath/York in the evening.

Google maps might be different a bit from the actual direction.

isn31c, i found that the certain guesthouse is nice but require at least 2 nights. I notice some guesthouse prefer 2 nights, not one night. Which means that i have to adjust the itinerary.

Is one day or 9:30am to 4:30pm sufficient to visit York Minister and York Castle Museum?

That is a far better paced itinerary now.

isn31c, i totally forgot that Thursday-Friday is the least busy day for France to visit certain places. Which is why I have to cram train journey from Edinburgh to London to Paris. How?

Firstly I'm not sure why you have to leave York at 4.30. There are trains to Edinburgh way later than that.
Secondly in York I know the Bar Convent does one night stays. It's impossible to get lost going there - turn right out of the station round the corner and It is at the next road intersection.
Opposite is the budget hotel Premier Inn Blossom Street North.

Thirdly with the time constraints you have for Edinburgh to Paris, and if I didn't want to fly I would investigate two alternatives. Neither will find any favour on this forum, but they are valid alternatives which deserve to be known about.
1- onward train from St Pancras to Newhaven changing at Brighton, overnight DFDS ferry from Newhaven to Dieppe, train Dieppe to Paris.
2- Overnight flixbus from London Victoria via one of the three ferry routes from Dover or the Channel Tunnel.

Firstly I'm not sure why you have to leave York at 4.30. There are
trains to Edinburgh way later than that. Secondly in York I know the
Bar Convent does one night stays. It's impossible to get lost going
there - turn right out of the station round the corner and It is at
the next road intersection.

Oh, i mixed up with York and Bath. I know travelling from Bath to York take up 4.5 hours while travelling from York to Edinburgh take 2 hours. So i decide to depart from York to Edinburgh at 5:30pm or 6:30pm instead of 4:30pm. Plenty to see around in York.

1- onward train from St Pancras to Newhaven changing at Brighton,
overnight DFDS ferry from Newhaven to Dieppe, train Dieppe to Paris.
2- Overnight flixbus from London Victoria via one of the three ferry
routes from Dover or the Channel Tunnel.

Hmm..I think i might miss the mention of ferry in RS travel book. I re-read RS' London travel book and find it. No mention in other Great Britain and England book at all. Excuse me for asking.
DFDS ferry - https://www.dfds.com/en?

I feel that it is complicated. Ferry to Calais in France for 1.5hours. Then take a train from Calais to Paris. Lots of hassle. This route will tire us out. I intend to go to Gare Du Nord in Paris via Eurostar.

I realised that i forgot that visiting Versailles on the weekends are the most crowded so i have to avoid weekends. I have to go there on Friday.

If i leave Edinburgh for London at 12:30pm or 1:30pm and i estimate my arrival in London at around 5pm or 6pm and leave for Paris on Eurostar at 6:30pm or 7:30pm. Is it feasible?

Opposite is the budget hotel Premier Inn Blossom Street North.

Incredibly cheaper. I wish i chose this but already chose the other option. :(
My heart aches. This premier inn branch is available in Edinburgh?

"i leave Edinburgh for London at 12:30pm or 1:30pm and i estimate my arrival in London at around 5pm or 6pm and leave for Paris on Eurostar at 6:30pm or 7:30pm. Is it feasible"

You need to check in for the Eurostar 75 minutes prior to departure, which for a 7.30 departure is 6.15. There's a but of leeway, but remember you have security and French passport control at St Pancras, and evening is busy. You need to allow some time to transfer from King's Cross to St Pancras (they're right opposite, but give yourself a few minutes to walk). That means a 5pm or even a 6pm arrival is technically feasible, but you can't set your watch by UK trains. A delay, train breakdown, track problem etc - they're all reasonably common. I wouldn't take the risk myself...

The walk from York station to the Minster takes 5 minutes. Then down to the Castle takes 10 minutes. Medieval cities were very small!

As for roaming around York for the day, there are plenty of lovely outdoor spots to walk and sit and take in the sights (including the city wall), but hopefully you are planning on Spring/Summer/Early Autumn rather than the depths of Winter.

Premier Inna are available right across the UK and there will be options in Edinburgh. They are all good value for their standard but not all will be very cheap. As always location, location, location.

As regards the ferry option yes you have the correct website but DFDS don't take foot passengers on their Dover to Calais route. Only P and O do. However coming down from Edinburgh I doubt you could make a same day connection into one of those sailings.
I don't think Rick even mentions the Newhaven to Dieppe route. If he does it may be under the old name of Transmanche Ferries.
Via Newhaven is better for an easier transfer than at Dover (300 metre walk from the station at Newhaven, and shuttle bus at Dieppe), and a time saving overnight crossing, just generally a far easier port than Dover.
The fundamental issue is that leaving Edinburgh at lunchtime a Eurostar connection is fraught with problems, very undesirable.
This is as tight a schedule as you can get, so thinking out of the traditional Eurostar or Calais box is needed.
More details are on the Man at Seat 61 website - have just checked.

Not sure if I am too late to add my ideas…but here goes!
Visiting in Europe is wonderful, but to really appreciate your chosen cities, you need more time.
It would be my suggestion to divide your itinerary into two different trips altogether!

Ghent-Brusselsetc is a great part of Europe. With more time on that side of the Channel you could even add on Rouen or Amsterdam!

The UK is magnificent, and there is SO much to see and do. I would suggest that you fly in to Edinburgh and home from London, or vice versa.

Also, your first day will be a write-off, energy-wise. So don’t plan on any intense touring. Instead, consider a day to wander the town, sit in cafés or on a terrace, and soak up the local vibe. Or take in an outdoor concert in a park, to clear your head of air travel blahs! You will enjoy the rest of your trip much more, if you you are not “running on empty”.

Have a wonderful trip!

The sights in Bath can be navigated on the Hop On Hop Off bus.

isn31c, Thanks so much for your excellent tips and useful info. I appreciate it a lot. I need to digest info because I'm not familiar with cities.

If i read properly - from london to dover by train, then take a taxi to the ferry station and then take ferry there to Calais and then take train to Paris, correct?

manager, yup UK is magnificient. I already visited part of UK last year on my own. This time, i visit UK with my family kin around.

The sights in Bath can be navigated on the Hop On Hop Off bus.

GBP$21?

Yes, the HoHo in Bath, run by Tootbus, is £22.05 if booked online, £24.50 in person. It has both the city centre route and the route into the countryside at Claverdon Downs,+ 3 self guided walks on their app.

Re- the Ferry option, that is via a place called Newhaven, not Dover.

If you wanted to go via Dover the schedule is-
Edinburgh depart 0800, Dover 1414 changing from Kings Cross to St Pancras, taxi to the port, check in at 1510, depart at 1640, Calais arrive 1910, taxi to Calais Ville station, depart 2032, Paris Nord arrive 2248.

I would want to leave Edinburgh at 0700 to give myself headroom in case of delays.
Via Newhaven you can leave Edinburgh at 1330.