Definitely live North London / north of London if he is working in St Johns Wood. Surrey / Lewes would surely be a bad plan.
You need www.commutefrom.com, which helps you identify what is on the right tube or train line for your commute. I know you say you don't want to live outside actual London, but in fact commuting times can be quicker from outsid London if you are on a fast train line, compared to within London, but on s much slower train. Eg I lived outside London, but my train journey is only 20 mins into Euston.
You will really really struggle to get 2 primary places plus a secondary school place if you move to St Albans, which has been mentioned more than once on this thread, after the schools' deadline. Schools there are horrendously over subscribed. You would need to start by finding a school with places, and then find the house, not the other way around. Presume from your OP you actually need 3 primary places, before your DD goes to secondary school?
The issue with needing school places out of the usual time is that anywhere really nice to live (eg St Albans, Tring, Harpenden) is going to have massive pressures on school places, so you may have to compromise on location in order to get the school places.
With that budget you could afford a really nice house in Watford...? Not a beautiful place, but very well equipped for families (parks, big shopping centre, leisure centres, cinema etc), and much more value for money in property than nice bits of N London or St Albans.