Monday, May 26 is a bank holiday, and that whole week is spring holiday for English schools. So there will be a lot of leisure travelers wanting to get home on Sunday night after visiting London.

Given the complicated pricing structure for British trains, it may be cheaper to buy two tickets: one from London to an intermediate point, and another one from there. I know you used to be able to do this without actually breaking your journey--I don't know if that's still true. There's a website devoted solely to recommending how to do this on various routes, but of course I forget the name and don't have it bookmarked. Sorry. I'd guess that one of the British FTers would know.