My dd aged 9 is over for a fortnight this summer and we have always had a tradition of checking out a new playground together.
She is quite fearless, so we are after something that can offer both a challenge to an older child and where a juvenile father who should know better will not stand out like a sore thumb (bless her, she is still not quite at an age where these things embarrass her).
We live in Bromley, but will gladly travel anywhere in London.
Presumably you've done the Diana playground in Kensington Gardens? If not, lots of it is aimed at little ones, but she could still climb the ship. Loads of dads there too. Busy (very in summer) & lively - so get there early in the day.
And there's one on Ladbroke Grove - Hornimans Adventure Playground - that my two love (though I've not been there with them) - water features, I seem to remember.
Various things for older children within the whole scene that is Coram's Fields (no grown-ups allowed without a child) near Russell Sq.