Surely your best bet is to jump on the train and then do the underground and book in advance a return ticket with tube travel ? Not sure what your train operator is in reading (I'm in Yorkshire) check out their website and you'll more than likley be able to book it online
Otherwise check with National Express if they go direct to London from Reading- usually victoria - and then tube it from there. I suggest asking because you may laugh but Reading to London might mean - Reading, Swindon, Cardiff, Birmingham London !!! If you get my drift !