Nope - there are no public grasscourts in London so far as I am aware. I did try on artificial grass once but that's weird and not the same anyway.
Do you play much?
Oh I really want to play on grass, in Canada I think we only have grass courts in Toronto and Vancouver and I have never played tennis in either city, never even been to Vancouver.
I play a bit, maybe 3 times a week on average but only in the summer so between May and September I guess. It is too expensive to play indoors in the winter, which is disappointing. This year I played my first tennis Ontario tournament, which I lost to the 8th seed pretty badly. It was a great experience though and got to see Daniel Garza play a few matches there, he was the top seed of the event (ranked 415 in the world).