What a lovely thing to do, I would have absolutely loved this when I was 11!
I go for afternoon tea in central London (where I work) with a friend 3 or 4 times a year and have been doing so for over 5 years now, lucky me!
I wouldn't recommend the Ritz, it felt very conveyor belt-like to us and the service dropped off an absolute cliff after the food was served, such that we weren't able to order the additional drinks we wanted!
My favourites have been the Goring, the Connaught, Claridges, the Langham and Fortnum & Mason. For an 11 year old, though, I think Fortnum would be the best of those (the service there was absolutely delightful in every way for one thing!) but you should definitely look at the themed ones. I went to the Alice in Wonderland at the Sanderson one several years ago, that was excellent and probably more kiddy-friendly (it's the only one I ever recall seeing any children at, for one thing, but my memory is ropey these days!)
I've heard great things about Sketch too, so have that one on your list for sure.
I'm sure you'll have a wonderful time wherever you choose, though, all the big, luxury hotels will give you a fantastic experience.