Bertram, yes, but it is also in the heart of seriously affluent West London with a serious academic blue-stocking tradition.
It uised to be where establishment London sent their DDs. Carol Thatcher, Rachel Johnson, Victoria Coren, Stephanie Flanders, Thomasina Miles etc, but has increasingly become the go-to school for London's very sucessful expartiate community.
Its an odd one. I know several Paulinas who have opted not to send their bright DDs there preferring the more straightforward approach of Putney High or Latymer Upper. My understanding is that the nearby G&L deliberately adopts a more caring/nurturing approach so as to provide a useful alternative. SPGS does seem to have a tough culture, and I have a good friend who was quite damaged by her time there. And as user1499173618 suggests, academic excellence is one thing, but not everything. The combination of the existing culture with parents used to a "class placement" approach to University entry, which brings with it a need to compete with classmates, appears to present a whole raft of additional problems.
Boys from the boys-school are called Paulines.