OMG so many ppl harping on about finding a less academic school, all schools being the same etc. They are not. I don't have actual advice for you as I'm in a similar situation to you.
Coming from your average prep your child will already be a year advanced in most cases. There will be a lot of boredom to factor in. Your child will be well versed to working hard and discipline if they got to round 2 st Pauls. We didn't do enough research moving from our prep, and have found the peer groups for ds and dd to be lacking. Our son in y2 for example can write stories has read harry Potter, ( only book 1 so far ), can draw, have a fluent conversation and is in a class where the teacher has just started to show children how to join their writing and have started read full stories. He is bored and we are worried. He wasn't the top of his class in his prep, now I think he's a able as all of the year 3's. Don't even get me started on my older dd....
Apart from reading a book at bed time we have never tutored or done homework with them etc. This is literally the level your average prep school is at.
Maybe look for a school with sets? This was suggested to me and i like the idea. I don't know what age sets start from, but putting our kids in a set with children who are actually willing and able to study would be better than our current " happy " school.
I have just taken out a subscription to the good school guide and I'm writing to the grammers ( council ) I'm interested in to get info on feeder schools. I think this is the best bet for us. There are also private 11+ tutoring outfits that may have a lot of this info. For example I think it was Atom, they can tell you how many children have joined each grammars from state vs private, I would assume they will have a list of state feeder schools. We are currently researching grammars for our dd, and will enroll with one of the tutoring outfits to get some proffesional advice. Might be worth a shot for you aswell??
The minute you ask for this sort of information in the state sector ppl think your pushy and get quite defensive, but the reality is if you have a really bright kid like yours is, well they need to be kept busy, interested, and motivated.
All the info is there somewhere but finding it is hard, it's almost as if being successfully academic is an embarrassment. I'm not looking at London otherwise I'd send you my meagre findings.
Good luck, I think in and around London schools should be more used to being asked about their academic output / destinations.