Your intuition that numbers to SPGS from state school are very low is actually right. If you add up all the girls who get in from prep school, the number of places remaining for state school applicants is actually quite low. Even from most prep schools, at the most one child will make it. If you add up the places taken up by girls from Bute House / Kensington Prep / Falkner House / Glendower Prep, and then look at all the prep schools that will send 1-2 girls to St Paul's, it looks like a maximum of 20% could come from state school at SPGS. That said, I think the percentage of state school pupils at Putney High, NHEH or Latymer Upper is much higher.
You have some data on SPGS and Latymer Upper feeder preps here and that gives you an idea of the numbers:
http://www.londonpreprep.com/2018/08/spgs-feeders/http://www.londonpreprep.com/2018/08/la ... r-feeders/