prepare a simple hamper but on your balcony or roof at night.
close all the lights and have candles, preferebly on a clear night in the summer.
with small bites.
cheap champagne and nice food :)
One of the best dates I have ever been on was when the man I was (and still am) seeing took me to regents park and we hired a rowing boat out on the lake...he'd also managed to sneek in a cheap bottle of plonk (which isn't allowed wink wink nudge nudge!)
It was so fun and spontanious...and unlike most of the normal average dates! probably best to wait until it gets a bit warmer.
Or you could go to portobello street market on a saturday. Great fun, you don't have to buy anything, and it's also not to intense as you can always get 'distracted' by an antique if a 'long silence' is hanging over you!!
Also you could check Time Out Magazine for Free Concerts, and the BBC Ticket Web site for free tickets, Hat Trick Website has tickets for Comedy and Drama shows too.