Does anyone know the names of schools in 1870/71 London (potentially near Brixton) where wealthy Americans traveling abroad would enroll their sons?

I am looking for schools in the London area operating in the years 1870/71 at a minimum where Americans traveling at length abroad might have placed their teenage sons to further their education. Specifically schools where the boys could board. I also believe the school I am looking for would have been near or in the Brixton area or perhaps Brixton was part of the name of the school?

This list of English endowed schools by county from the early 19th century is organized by county/shire, including Surrey (location of Brixton) and the adjacent Buckinghamshire and Middlesex/London counties, which include among others the town of Eton and its eponymous College.

Surrey:
-- Wilson's Grammar School, Camberwwell (Most likely possibility - see below)
-- Farnham Grammar School
-- Royal Grammar School, Guildford
-- Kingston Grammar School
-- Saint Olave's Grammar School
-- Saint Mary Overey Grammar School
Berkshire:
-- Abingdon Grammar School
-- Childrey Grammar School
-- Newbury Grammar School
-- Reading Grammar School
-- Wallingford Grammar School
-- Wantage Grammar School
Buckinghamshire:
-- Amersham Grammar School
-- Aylesbury Grammar School
-- Buckingham Grammar School
-- Eton College
-- Royal Grammar School
-- Marlow Grammar School
Middlesex (Now wholly incorporated into London County I believe):
-- Enfield Grammar School
-- Hampton Grammar School
-- Harrow grammar School
-- Highgate Grammar school
London:
-- All Hallows Barking Grammar School
-- Charterhouse School
-- Christ's Hospital School
-- Mercers' Chapel Grammar School
-- Merchant Taylors' School
-- St. Paul's School, London
-- Westminster School

Wilson's Grammar School was located in Camberwell from founding until 1975. With the centres of Camberwell and Briston barely 2 km apart, that would likely be the school closest to Brixton at the time of interest.