There are 4 main casinos to play at in London. Aspers, The Vic, Empire and The Hippodrome. 2 of these cardrooms are almost directly next door to each other in Leicester Square. Your best bet for a place to stay will be in the Leicester Square area simply due to the options you'll have around there.
When you're over here if you fancy a change of pace and want to drop in on some private games give me a shout, I run games most days of the week in the city.