£400k for a cash purchase - where would you buy?

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We've been trying to buy in London for a while. We're getting so frustrated with the limited options and prices that continue to rise at a ridiculous rate. We're starting to wonder if it would make sense to just go for a big change and buy in a completely new area where we'd have no (or little) mortgage. Our kids are about to finish primary, so it could be a good time for a change. Commute not an issue thanks to remote work options.

We'd want a nice town or city with a decent high street, good transport links, good schools, progressively-minded.

Where would you buy for under £400K?

Look at Market Harborough, my son moved there 3 years ago and loves it there. Town has train station, an hour into St Prancas. Plenty of independent shops and cafes/restaurants and more upmarket chains (including Joules, Mint Velvet). Secondary schools have Ofsted rating of 2. Supermarkets - Waitrose, S'bury, Aldi and Lidl. Check it out!

I just bought a 4 bed detached 2 year old house in Banbury for just under £450k. Just an hour away from London on train. Not far from Oxford and Birmingham and not to far from the Cotswolds for a day out