The heads and teachers at these high performing primaries are no doubt working hard and effectively, but move these schools to a less affluent part of Lewisham and their performance would drop.
Children with a stable and rich stimulating home-life will do better. There is no mystery here.

If they flattened part of the Tewksbury lodge estate and built a smallish secondary school, I think it might well genuinely be ranked within the top 10% schools in the country.

As it is, there are not enough privileged children in the area to dominate a large secondary school - the 2 main secondary schools are much more representative of Lewisham - an inner London borough with all that implies - (various levels of poverty/deprivation being the key).
And naturally the secondary schools' focus is on the majority of children who have been underachieving/are likely to underachieve (and they do this job very well, I understand).

I'm not saying the children from the elite primaries cannot survive and prosper at these secondary schools - their home advantages should see them through, and maybe a dose of local reality makes a young person more rounded. But academically, as a minority, they will not reach their potential in my opinion.

Incidentally does anyone have information on home tutoring?