I took my six-year old niece to London for the day a fortnight ago, crisgal. We went to the Natural History Museum (free) and then to their Butterfly Tent out on the lawn (£3.50 each for entry), and she loved both. Then we went to Buckingham Palace and to lunch at the Rainforest Café (http://www.therainforestcafe.co.uk/), which is expensive, but the look on her face... :) We went to Hamley's Toy Store aftewards and were in there for about three hours, as she wanted to watch all of the displays they put on with the toys and make sure she'd seen everything they had before she decided what to spend her pocket money on. After that, we went for ice creams in Trafalgar Square. It was a gorgeous day and she loved the fountains.
It was her "best day ever", apparently, if that helps, but not sure if there'll be a difference in what they like, given your daughter being slightly older. Hope you have a fab time with her. My niece slept until midday the next day. :)