I too would like to recommend Chestnut - we too came from an independent - the school is virtually brand new, with masses of outdoor space and sports facilities - the teaching staff are dedicated and flexible in approach to lessons and kids’ attention span - music and art and languages are great, but so are the sciences - food is good - pupils are a realistic representation of london, unlike some private schools - good extra curricular programme - and I really feel they focus on kids’ abilities and interest when it comes to guiding them on what to do after A levels.
Joining Chestnut was an eye-opener and I am so glad we cancelled our private school place despite having paid deposit. And yes, private kids going in will find the going easy in first year, but it allows them time to find their feet and make friends. And do sign up for Art or Language test. The latter is not about ability to speak a foreign language (though it helps) but about understanding how languages work, ie if one tree is xyz in foreign language, what would 10 trees be in that language. We did it and got on waiting list for language spot and so many on list dropped out for preferred school choice (silly them) that we got in without having to worry about catchment.