Good luck with the test prep.
I've got recent experience of the school as a parent. What would I say in response to some of the comments and questions:
(1) I'm not really sure about the "two schools in one" suggestion - certainly most teachers teach both the top and middle [I'm less sure about bottom but I expect it's similar] streams and what they're taught is broadly similar.
(2) There's [to my mind] a significant overlap in academic standards between the top and middle streams - it no doubt varies year by year [since e.g. in the past there have certainly been variants on a 'top extension' class rather than them all being roughly equal, something like that may well be brought back in the future if it hasn't been already]: the top 5, maybe even the top 10 kids in a typical middle set class will be often be stronger than the bottom 5-10 in top set. And then when they get to GCSE a not tiny number of subjects aren't even setted, everyone from all streams is thrown together, which makes you wonder what the streaming was for other than segregation [which many parents presumably like?] as an end in itself.
(3) There probably are toxic elements to the streaming. There are very stark, jarringly obvious, differences in the ethnicity and socio-economic class of each stream. You'd nearly always be able to guess what stream a class was from just by eyeballing the kids lining up together.
(4) I don't think movements between sets are based on school CAT tests, more all-round assessments of academic progress, which may or may not be objective. At least sometimes a by-product of the in-year movements between sets is to even further homogenise the backgrounds of the kids in the classes.
(5) Every year's intake does seem to end up with a fair sized 'in crowd' of kids [mostly white, upper middle class] who take it upon themselves to try to recreate old episodes of 'Skins' on Ch4, with a lot of drinking and worse starting in year 9 [or earlier]. More so than other schools in the area? I really couldn't say. I suppose it's quite rare for a London state secondary to have so many kids from relatively moneyed, relatively liberal [white] families. I can't say I've heard of any unusual number of outright disasters resulting from these behaviours, but others might.
(6) No-one's mentioned it but if it's your kids' thing then music and sports are both taken far more seriously, to a far higher standard, than at I daresay any other local 'comprehensive'.
(7) The school fairly plausibly claims to get good academic results/progress for kids in all of the streams, from all backgrounds. I wouldn't pretend to be nearly familiar enough with how these things are scored to comment on the veracity of these claims.