The UK needs to forget the idea of "green belt" and think "grey fingers" instead (or "transport corridors" if you want the more technical term).
Basically, the idea is, you create a rule that says "You can build housing fairly easily AS LONG AS IT IS WITHIN XX MINUTES WALK OF A RAILWAY STATION. (Anything else is hard to do)."
Hence, "grey fingers." Housing gets concentrated along railway lines, branching out from cities in a formation that looks like a hand with spread-out fingers.
This is roughly the way building is handled in a lot of other densely populated countries where public transport is an awful lot more functional than it is in the UK.
This way, you
a) make sure that housing is near public transport, which makes it far easier to keep tight controls on car use.
b) create an incentive for actually building public transport.
You can also create systems where companies building public transport can use land immediately around train stations to build shops and services, and profit from these. Again, it ensures that any new developments are public transport-oriented, and avoids these ridiculous housing estates stuck out in the middle of nowhere.
The UK is a densely populated country and needs to start acting like one. There needs to be proper action on requiring all new developments to be oriented around rail, and then cracking on and building proper (electrified) rail to make this possible.
It would also help to improve leasehold laws and liberalize the rules around apartment building to allow generously sized apartments with nice big balconies and shared green spaces, offering a great standard of living. The UK houses a very low % of its population in apartments and this needs to change. You are a densely populated country. Densely populated countries either need to accept taller buildings and more apartment living, OR your houses will increasingly resemble rabbit hutches with tiny weird gardens jammed in at peculiar angles and too small for children to usefully play in, and cars jammed into every inch of the development because there is no way to do anything whatsoever without using a car.