10 days in England/South Wales. Need help with Itinerary!

You have ten days on the ground (if I read your post correctly) and seven destinations across a wide (for England) area, including one of the world's great cities. Trying to "see" them all will mean traveling between places almost every day, i.e. checking out of hotel, going to station, riding train, going to next hotel, checking in. Lots of front desks and stations and trains, not much time for anything else. It's common to spend half a day just changing locations this way. I hope you'll pare down your itinerary to something like London/Oxford/Bath or London/Liverpool or London/Cambridge/York. London alone could fill your whole time. Cambridge, Oxford and Bath are each plausible day trips from there, you might pick one.

I'm reminded of this post a couple of years ago, https://community.ricksteves.com/travel-forum/general-europe/least-helpful-rs-advice, there wasn't a lot of love for the advice to head to Bath first which is what RS suggests. I think that goes for a lot of places after a long overseas flight. Our first trip to England was in 2018 and we spent a week in London and then 2 nights in Bath and finished with 3 nights in the Cotswolds. I think London is a great place to start and recover from jet lag before you start hauling luggage for short stays elsewhere.

Your wishlist is a good one but too long for 10 days. You could easily spend 10 in London. I'd suggest you prioritize what is most important and plan like you'll be coming back. I think Wales and Liverpool are too far for this short of a trip.

Dick is correct - to visit everywhere on your list would involve moving on every day, getting an afternoon and evening in a place then moving on for the same the next day. Unless the industrial dispute gets settled, continuing train strikes is a strong possibility.

By mid October, there won’t be much colour left in Cotswolds gardens, so I would suggest dropping this area. It’s also easier by car.

For many first time visitors, five days is the minimum time suggested to see the main highlights and you could easily fill your time here including a couple of day trips to say Bath and Oxford/Cambridge.

Travel styles vary, but after a long flight, I couldn’t think of anything worse than trying to get to somewhere that wasn’t on a direct train route e.g. Bath.

You need to prioritise what interests you the most. I would suggest London plus two other places, assuming you need to be back in London for your return flight. Best combinations for rail travel would be Oxford and Bath or Cardiff and Bath or Liverpool and York. My preference would be Liverpool and York as you would get to see more of the country whilst on the train and they are both cities with plenty to see. But, it’s not my trip!

Cardiff, whilst interesting, IMO isn’t as interesting as the other places on your list. I think the best part of South Wales is St David’s, as the setting is stunning, but it’s more remote.

The last two weeks of October are school holidays, so places will be busier.

As suggested above, you will need to pare back the number of destinations and focus on an itinerary that
is doable in 10 days. London can easily take 3-5 days just to scratch the surface. That leaves you with 5-7 days elsewhere. Realistically, you could work in Bath, the Cotswolds, Cardiff and Oxford if you are OK with staying just one night in four out of five of those locations. They are proximate to one another and you could travel by train. My family did a similar itinerary by car ( Bath, Cotswolds, Chepstow. Wales and Oxford) before seeing London at the end of the trip). We were not prepared for the differences driving in Britain entails and trying to do a fast car tour outside London in only a week is not something I would recommend.
Liverpool and York can only be seen in your ten-day timeframe by eliminating most of the other places on your itinerary.

I agree that reducing your scope will result in a more enjoyable trip. I've taken Rick's suggestion to start in Bath and believe it's sound advice. It doesn't take much effort to get there after arriving at Heathrow, and it's so compact that you can see a great deal with minimum effort. It's an easy train ride from Bath to Oxford - and Oxford should be worth two nights. From there it's easy to visit Blenheim Palace, and you could most likely find a tour to venture into the Cotswolds for a day if you really want to see the area. Then London for the remainder of the time. You'll experience more by slowing down.

I agree with those who say you need to do some serious pruning and prioritizing. I just got back from a trip where I spent 2.5 weeks in Wales alone. In 2016 I spent 6 weeks in England and Scotland.

Look at a map. This is a pretty good one:
https://www.worldatlas.com/maps/united-kingdom/england

You can see that Liverpool is NW of London. York is almost due north. Cardiff and Bath are slightly SW. To get an idea of travel times, routes and train companies use Google Maps.

For example, I took the train from Cardiff to Heathrow on August 23. It was Great Western Railway for Paddington. If I'd stayed on all the way, it would've been 2 hours.

According to Google Maps, from London to Liverpool is 2.5 hours plus via train. From Cardiff to Liverpool is 4 hours plus. From Liverpool to York is 2.25 hours plus. And from York to London is about the same. You can look up the options for exactly where you want to go and when.

These are not trivial travel times, especially when you need to be at the station in advance before and get to your lodgings after.

Only you can decide what's drawing you to all the places you list and try to figure out how much time you need to devote to what you want to see and do.

Having been to all those places except Liverpool and Oxford/Cambridge, I'd drop Cardiff unless you have a burning desire to see Caerphilly Castle or St. Fagan's National Museum of History. Either of those is about an hour round trip from Cardiff on the bus and at least 2-3 hours to visit. Keep in mind that you'd need to coordinate the bus schedules with their closing times.

I'd drop the Cotswolds which is over-rated in my opinion, even if you take a tour. I've been to Bath twice. If you're taken by its history, it's worth a day sandwiched between 2 nights or maybe a day trip tour.

York is interesting with the Shambles, York Minster and possibly the Yorkshire Museum if there are events there of interest to you.

The last time I was in London, I did save it for the end of my trip. I spent 7 nights in an apartment, giving me 6 days on the ground to do and see things leftover from my 2 previous trips there.

Although you didn't list it, with a Beatles fan along, I assume that you're planning to visit Abbey Road Studios even if you can only be outside:
https://www.abbeyroad.com/crossing

For all the other places on your London list, you need to check their open hours for the days you might be there and realize that every place you've listed will take from 1-2 hours to visit. If you're going to the British Museum or the National Gallery it could be longer for each.

Also, the Tube will likely be faster, but you obviously don’t see anything of the city when you're underground. Just sayin'.

First of all, you will love England. But you will love it more if you aren't trying to do what I think is impossible (except to just drive through some destinations). I have been to all the places you list except Liverpool and I have only been to the Cotswolds on day trips(and have no desire to rent a car to spend more time there). Personally, I would choose York and Cardiff. Both of these cities are an easy and not too long train ride from London. I would spend 2 nights in each of those cities. If you insist, two nights in Bath and take a Mad Max day bus tour from Bath to Cotswolds. That would leave 4 nights at end for London. Cambridge is an easy day trip on the train from London, but that doesn't leave you enough time for London. You will use up at least 1/2 day every time you move from one city to another, for train time and checking in and out of hotels, and this may be a huge drain on your energy, especially since all of this will be new for you. Do not make the mistake of thinking that you can do this because tours do this-on tours, someone handles all the logistics. Unfortunately, you also need to monitor this forum to read Nigel's posts about train strikes that may affect your plans.

We did a four week drive tour of England (no London) and South Wales in 2017. It was wonderful. You only have 10-12 days.

You plan to do London, which will give you about a week. Forget going to York or Liverpool. York is wonderful, not so impressed my Liverpool, but geographically they are away from the south of England and south Wales.

I suggest visiting Oxford, Windsor Castle, Bath, Cardiff (Wales), Tenby (Wales) and St. David's (Wales), and the Cotswolds (we used Chipping Camden as our base to visit the Cotswolds, Oxford, Blenheim Palace and Stratford Upon Avon.

Here is my detailed review that may help you in planning.
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

You need to book tickets in advance for the historic sites in London that you want to visit.

Prioritise what you want to see or rank your choices 1-6 and choose two or three from those. You can always add stops along the way.
Don't suffer unnecessarily by excessively moving about but you do have options and many possible combinations of 2-3 destinations.

I don't blame you for wanting to pack so much in. England is am amazing country to visit. We have visited England twice and primarily stayed in London. Both times we planned a day trip by motor coach to see first, Bath, Stonehenge and Windsor Castle and this last time, Oxford, Stratford Upon Avon and Warwick Castle. It is a very long day and some stops feel a bit rushed but we weren't disappointed. We made sure to leave a little time for rest the day after, and overall this afforded us more time to see all that London has to offer. We will be back in early December and both Liverpool and Cardiff are on our list!