I have attempted to purchase train tickets on the British National Rail website. For some reason, the transaction is not completed regardless of which credit card I use. I've had no such problem with Heathrow Express or London Eye or any number of other purchases. I'd certainly like to have my train tickets in advance. Anyone with similar experiences?
Scroll down and read Edwin's post from 1/26/11.
Try booking at www.eastcoast.co.uk. You can book trains for any UK train company on that site and it accepts US credit cards. If you book about 60 days in advance, you often can get discount fares for longer rides.