Non-Touristy things to do in London

[LightsOnComeOnIn]

I'm taking my nearly 16 year old sister down to London next weekend, she's always wanted to go to Madame Tussauds so we will go there but we're interested in doing some non-touristy things, would anyone have any recommendations??

go round someone's house?

Big parks to walk around. Art galleries, strolls by the river, Covent garden shopping?
But those are still too touristy?

so what did you do?