Go for a cheapish meal in Brick Lane, check out any of the churches, Science museum and the others around South Kensington, Imperial War Museum is nice but I can't remember if it's free.
There are also a lot of walking tours you can do for free i.e. Jack The Ripper in the East End, so look those up. Not for everyone but it's something different, just please don't walk up and down Oxford Street.
Oh and if you have time and you're in London on the weekend check out Speakers Corner in Hyde Park. The black guy with all the beads is funny - 'the white man is the devil!'
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