I would suggest you try:www.virgintrains.co.uk. In their "buy ticket" section, I tried Euston to Edinburgh Park (one of the edinburgh stations). The date I entered was Aug 5th. A standard advance single would be 72 pounds 50p. There are several trains on that day. The one I chose left at 9.40am arrived Edinburgh 14.56. Just over 5hrs later. It is not direct. There are 2 changes. If you want to book 1st advance single, the price is 125pounds 50p. Same train.Book your seat at same time.
Having just recently used the first class travel Euston to Manchester (42pounds 50p) I can tell you, it spoils you for any other train travel! Virgin trainshave their own 1st class lounges at the stations-free coffee/tea/snacks. They also have a great menu on board. depending on the time of day, you can choose from breakfast, lunch or dinner(included in the price of the ticket) There are also all day snacks and beverages. There are plug ins for your laptop and/or cell phone by the seat.
I am a senior. The train staff were great.I was very comfortable and enjoyed my train journey very much!
The rates may be lower in October ?
If you are thinking of going by car, I can tell you that the price of diesel in England, in June, was 1pound.30p ($2.60 Canadian a litre!) That is twice what we pay here! Also, the motorways are packed with traffic. So, it's possible to spend time in traffic jams!
Hope you have a wonderful trip, which ever way you choose to travel
Shirley