What is there to do in London for the day that is cheap?

I'm planning on going to London for the day sometime around about 20th Feb wih my boyfriend, I've managed to find bargain tickets to get there and back, but I don't know what to fill our day with that is fun. I have a very limited amount of money, as I don't get payed until 2 weeks after, so I want ro have a good time, but be affordable