Near us (South London) the price difference between a 2-3 bedroom house in particularly good catchment area vs. an average one is at least 100,000 pounds, sometimes more...

Which makes it very clear that it's priced based on private school costs, given that the private schools near here costs ~10k/year (huge variations, but that's roughly it for 2-3 of the most popular ones)...

I've had the argument with my ex. over my sons school too. I had halfway given in and agreed to send him private, but we ended up sending him to the local school two doors down from me instead of 40-60 minutes travel to the nearest suitable private school, thankfully. But we'll be having that argument again over secondary school, I'm sure.