Hmmmmm
I think peoples interests are so varied that someone will do at least one of the types of things suggested. (Like rope, cups and balls)
Perhaps a trick involving a prop you're going to find in the bar? that might be too soon for this saturday though, I know I'm struggling for time.
Coins Across?
Omni deck stuff?
deck vanish stuff?
Card at Any number plot as suggested before
edit: for cheapish hotel deals check out the following (its relative, london is always expensive or get so hammered that someone has to look after you and gives you a place on the sofa)
www.londontown.com
www.hotelclub.co.uk
www.expedia.co.uk (believe it or not they come up trumps once in a while)
For real B&B stuff look for places like Belgrave road (walking distance from victoria station.
The best deal I ever found at the strand was £95 for the night for a single room.