I think what the people who don’t want to live in London don’t understand is that, for some people (myself included), the big house, the swimming pool, etc just isn’t worth it.
Generally, people choose london because of the community, which isn’t quite the same outside of it. London is a truly diverse city, a place where people from all over the world choose to live.
Lots of areas outside London tend to be homogeneous. There’s nothing wrong with that, if that’s what you want, but if it isn’t - then it’s worth the expense to stay in London.
London also has excellent schools as young, ambitious teachers tend to (not always!!!) want to live in the city.
You’re either willing to pay the premium to live in London or you’re not.
The OP can afford the neighbourhood she wants. Why keep showing her cheaper ones?
And, to reiterate what others are saying, both those houses are in the catchment for great schools (primary and secondary) and you won’t need to move again, and you won’t need to pay for private school.