If at all possible, it would be much simpler, and most likely quicker to fly. Without knowing your dates and arrival times you will generally have to change at London Paddington, cross London, to Kings Cross then another train to Edinburgh. There are variations. Best site to check train times and prices is thetrainline.com. Time will be in region of six hours. Hope this helps. Good luck. BTW the earlier you book trains the cheaper they are, booking on the day is always more expensive.
