Help with train travel in UK

Although there are some exceptions, the price differential on UK rail tickets between buying far in advance and buying at the last minute can be truly massive. It can have a huge impact on the overall cost of your vacation. When tickets initially go on sale, some are available at a bargain price, but there's no way to be sure how long those good prices will last. It depends on how quickly other travelers snap up those tickets. Once the cheap tickets are sold, you're stuck with costlier ones. You potentially have some room to maneuver by choosing less-popular departure times (and mid-day is often a good option), but on a short trip you may not have that sort of flexibility. It would be great to get your itinerary pinned down so you can grab the rail tickets you need. But those bargain tickets are nonrefundable and nonchangeable, so check to be sure you're not bumping up against some big-deal event in one of your target cities that causes hotel problems for you. I've verified that Edinburgh Festival isn't until August, so that's one thing you don't have to worry about.

I can't comment on Uber, but in cities of any size, there should be taxis waiting outside the rail station. In small places (perhaps Moreton-in-Marsh in the Cotswolds would be an example), you might need to summon one. It certainly wouldn't be an issue in York, Edinburgh or London.

I think that the best way of doing it is like this:> Don’t go from Leamington to York as this way you will be repeating the section between York & Edinburgh north and then southbound. Take your hire car to Leamington Spa and then buy a ticket (on the day) into Birmingham (New Street is the main station but some local trains from Leamington Spa go into Moor Street). Anyway, this ticket will cost you £7.30 (into Moor Street) or £10.50 into New Street from Leamington Spa. Now, it is worth a little walk through the centre of Birmingham (if you are so inclined) as it has many fine Victorian Buildings.

Now go to www.nationalrail.co.uk and put in for BHM> EDB. I just checked for a date well in advance = 22 March and found a direct Virgin Train departing Birmingham New Street at 12.15 to arrive Edinburgh at 16.22 for a price of £27. So, doing it this way, you use the shorter western route between Birmingham & Edinburgh. (Some services require a change en-route - click ‘details’ ).

Then check out the fares for EDB> York and stay in York for maybe 1 night on your journey south. Then check out for YRK>KGX (London Kings Cross) for your final journey. Pre-book specific trains about 11 weeks out for the cheapest fares. Buy on the day for the local hop.
Look at the rail map:>http://www.nationalrail.co.uk/static/documents/content/routemaps/nationalrailnetworkmap.pdf

www.seat61.com
The Man in Seat 61 knows all. Sorting out the rail network since it was privatized can be a challenge and he can help, especially on pricing strategies. Sometimes buying in advance from particular rail companies can save money. Any ticket agent can print out the tickets for most, if not all, your rides.
In my view, the ride in Scotland is worth staying awake for, particularly in the north.

definitely take a Virgin train rather than Cross Country from York to Edinburgh