Of course, this might be all 'academic' if DD isn't academic! Way too early to tell, but not too early to research.
Of course if she's very ordinary academically, that's fine with us, its all about keeping options for us.
We're both in our 40's , we've both had two careers, had our child late through IVF, we've built up substantial pensions. An inheritance when partners mother died paid off big chunk of mortgage. Partner will inherit a lot more when elderly father passes , hopefully not anytime soon.
We've Right Moved checked schools, looking at porting remaining mortgage to be near ( within 20-30 mins commute) to most schools, and its do-able. True a school like say Goldolphin is going to get us a smaller property for our buck than a school like Wallington High. We only need a 2 bed, as there's only 3 of us. The ship sailed on any more kids. No desire for big house , a nice garden flat is fine for us, also means our mortgage is a few hundred quid a month, leaving us a lot to save, etc, could easily increase mortgage if we really needed to.
So although a modest income (London-wise), we doubt we would qualify for much help, we would apply anyway. But we could sell our place and find another 2 bed without too much grief. We'd be savvy about it too, moving to somewhere like Tulse Hill for Jags instead of East Dulwich!
Completely accept if we had more kids, needed a 3 bed, all of this would be completely different.