DD1 is in Y1 and goes to such a school (although we're moving out of London in a few weeks) - from your post and what you describe, you could easily be living right near me (am in SE London!)
I won't lie, the school is Ofsted Outstanding but given she was unlikely to stay there long as we'd been planning an escape from London for some time, I was more concerned about the social side of her education. Would she be ostracised for not speaking the language of the majority for instance?
In her class of 30, there are about 3 or 4 children who are white British - the rest are an extremely varied mix, mostly African but some Eastern European and a few Asian countries thrown in for good measure. Most speak English as a second language. The borough is one of the most deprived in the country and the take up of FSM is 33%.
I needn't have worried. She has been fine, totally fine. Far better than I would have expected, and miles better than I was at my 100% white middle class village school. She's made loads of friends, and is an extremely popular child. One thing I love is that she just takes it for granted that people have different backgrounds and cultures, and subconsciously would not have a racist bone in her body - I was 19 when I left home and it was a real culture shock. I've made plenty of friends too, in fact none of them are white British at all. I actually found I had less in common with the local white British families in many ways - as the others were more likely to be better educated for a start, and have more similar views on child rearing despite the continents between us.
I also worried about the exact same thing you did - would all that help given to those who need extra help with English detract from giving DD1 the challenges she needs? The answer is no - it's made no difference. They've set her challenging work and she has absolutely raced ahead. Her teacher today told me she's at least two years if not more ahead and has been setting appropriate work for her, so I can categorically say she has not been held back. Basically the school is used to this situation and everybody is in mini groups in each class of similar abilities. So there is a very diverse range of ability in each class but nobody suffers as a result.
I'm actually really very sad to be taking her away from this school when we relocate as I don't think we will find a better one. I never dreamt I would find myself thinking that just over a year ago. In fact a diverse population of both race and class is something I'm hoping to find in her next school.
I hope that reassures you a little!