Traveling from London to Edinburgh

You could take the train one way from Kings Cross up the east coast then back to Euston next day down the west coast- at 52 minutes past every even hour.

Just take the train both ways. Easy peasy

There is no real time saving flying rather than taking the train, especially when travelling from city centre to city centre. By the time you have added on time to get out to the airport, time to check in and get through security and time to get through the arrival airport and then back into the city the time equation is about equal. You maybe could save a little time by flying into London City but those flights are usually more expensive. And flying is just so much more effort with journeys to and from the airport and getting through security etc. With the train you just turn up a few minutes before departure, sit down and get off at the other end already in the city.

isn31c's suggestion to go one way up the east coast and the other down the west coast is a good one, to see much more of the country. The west coast route is slower but you can speed it up by changing trains in Crewe on the way south. I don't think it works on the way north. The change in Crewe is very simple - get off train and wait on same platform for second train.

Sleeper car for the return trip? https://www.seat61.com/train-travel-in-britain.htm Full day in Edinburgh and then a full day back in London.

Personally, I find that train travel (have not done London to Edinburgh) not to be all that scenic. Lots of farms, factories and cities. Views often blocked by walls, hedeges and track-side buildings.

Please let me know if I'm wrong about this route as I am looking a multi-week UK trip in 2025.

I took the sleeper car once from Edinburgh to London and would not do it again. First, it leaves quite late. So if you don't have evening plans or accommodations you kinda have to just hang out and wait. Secondly, it really isn't that long of a trip. So you're there before you know it and there isn't really time to actually have a meal and sleep on the train. YMMV.

I like seeing the farms and the cities on the west coast mainline (Euston to Glasgow). The first stop isn't until Warrington Bank Quay usually and it's quite flat and rural up until then. It's scenic as you come up through the Lake District and across the border to Scotland. I like looking to see what the weather's doing, spotting livestock, seeing how the rivers are looking for fishing, admiring hills, that sort of thing.

I had not suggested the Sleeper because surely the idea of taking the train is to see the scenery. Down the West Coast you can leave at 1652 and be in London by 2215, and at 1852 and arrive at 0117. So although a very late arrival you get the whole day in EDI and avoid the very high cost of the sleeper.

But on the Sleeper do as you would in London- go to a restaurant, or the movies or the theatre first- then arrive at Edinburgh, go to the LNER 1st class lounge (which sleeper passengers can use from 2100 until boarding at 2300, then at Euston use the Sleeper lounge to freshen up and have a bit more to eat and drink before starting your day in London.
The train boards at 2300 prior to its departure at 2342.

Many train vloggers have done this run, check YouTube.

The Points Guy UK team did a train vs plane race, it doesn't go the way you'd expect.