I think it's important to remember that a lot of green belt isn't actually... green. A lot of it has development on it already.
That said, I'd strongly prefer building on brownfields, and on the "golf belt" (golf courses may look green but they really, really aren't. And they currently take up almost as much space as housing in the UK!). And I'd also like to see more densification of existing suburbs (putting low-rise flats in place of bungalows, adding extra stories to existing buildings, perhaps putting some extra buildings in places of garages). I would also like to avoid unnecessary urban sprawl. I see these horrid new-build housing estates on the edge of town and they seem so badly located and so lacking in services and in nice, sociable shared spaces.
It's important that people understand that there are trade-offs about building on brownfield and already-developed sites.
When we densify existing suburbs, we get moans about "dust/noise of construction" and "pressure on GPs/schools/whatever" (even though most schools have falling rolls these days). Infrastructure does catch up eventually (because new residents are not just consumers of services... they also work in, staff and pay taxes towards GP services and the like), but in the meantime there can be time lags and people have simply got to be patient about this. People also panic about "where will all the cars go?" and it may be essential to tighten up parking laws and for the area to shift more towards public transport and other modes of transport, to ensure that extra residents don't cause the whole area to become horribly congested.
And building on brownfield sites brings conflicts of its own. A lot of residents of suburbia and the countryside are all in favor of "Build on brownfield!" because they basically think this is a way of "putting those annoying people in a bin where I don't have to see them, while I get to hog all this lovely space and greenery for myself." They often suddenly become a lot less keen when the penny starts to drop and they begin to realize that "brownfield" tends to mean "car parks" most of the time, and that their ability to drive into town and park is going to start disappearing (this is starting to happen in places like Leeds, apparently). Also, if the UK shifts towards a more Continental/Japanese model where urban centers are full of apartments and people living there, those residents will want more walkable and bikeable centers and will start to push back against the suburban denizens who are used to being able to drive their SUVs in.
If we want to be stricter about avoiding green belt, it would also help if the British could try and get a bit more used to the idea of apartments (not for everyone, but perhaps for more people? More families?), and sharing a shared garden or local park, rather than insisting on detached homes with gardens for everyone. I live this way, and it can be a great way to raise a family if you have decent lifts, soundproofing and balconies. That demands a bit of a culture shift and also learning from other cultures that make apartment living "work."
The only other alterative is "tall skinny houses with many floors." I know some people here in Tokyo who have these; they are nice in some ways and it can be nice to have your own plot of land, but oh my goodness, people do get awfully sick of the millions of stairs! And you can't have a proper balcony.
Trade-offs, innit?