I can understand why you would do this. I went to a private school with an assisted place in the 90s. We got much more support than just 25pc and no remortgaging but it was still a huge sacrifice.However it was a rocket booster for me - first gen at top uni, good jobs etc.
However state schools were pretty dire at the time and I didn’t live any where near London.
Today i also really the impact of no family wealth behind me - only got mortgage in late 30s. Won’t inherit, have had to always work full time, despite children. I also didn’t really have any connections at school to help me in my chosen field as everyone did medicine, accounting etc.
So I would think really carefully. My DC are doing great in a London state school that has a very mixed intake.
Our tutors say they are ahead or at the same level as their prep peers in some ways.
The preps are doing more advanced stuff, which we are doing with tutor. The state schools are pretty is excellent at drilling the important fundamentals. They have fantastic opportunities- chess club, language club, singing with top choirs and teachers - all for free or a few pounds.
And there are loads of really good London secondaries.
Class or ethnic differences on London are more accepted than in other places. Everyone is different in some way! And a non middle class intake, doesn’t mean the risk of bullying is any greater.
If it was somewhere like St Paul’s or City of London I would consider your route. If not, unsure if it is honestly worth it.