I've watched many friends move out of London over the years, some further afield than others. Most needed to be within reasonable proximity to London for work. Tunbridge Wells, Reigate, Amersham, Newbury, Oxford, Guildford to name a few that are worth looking into. There is a great website 'life after London' that might help you reach a decision. We recently moved out to Marlow after 12 years in Clapham. We needed to be West of London for my husband's work, so struggled with finding somewhere close to London but that was still a bit lively.
There are plenty of primary schools and there is a fantastic local grammar as well as a very good state secondary (Great Marlow) and also plenty of private options close by too. Its not the cheapest place to move to if you want to be in the town itself and the houses in Marlow aren't huge (not a lot come onto the market but those that do are mostly are 3/4 beds with smallish gardens), but you can find large detached properties for far less than the price of an average SW London terrace a little bit outside Marlow if you are prepared to be drive everywhere. We were all so worried about moving out of London but love our new life and the kids settled into school quickly, making some lovely friends and they have so much more space to play, a kitchen garden where they grow fruit and veg and the highlight last term was the pheasant that kept laying eggs in the sand pit at night! So many great walks close by, the river with all of the activities that entails (rowing, paddle-boarding etc), lovely shops in Marlow with High Wycombe less than 5 miles away with a big shopping centre and so many great restaurants (not that we have been able to try many yet with lockdown!)
Good luck with your search!