I'm assuming "grey belt" means "previously developed land in the green belt", as distinct from greenfield land not in the green belt.
The greenbelt is a nice idea, but unless you believe the fiction * that there are vast swathes of brownfield land in town centres waiting to be built on, it inevitably means that people will want to build on land outside the green belt (i.e. most of the country's farmland).
Stopping individual towns merging into one is arguably the primary function of green belt, and most towns didn't bother (that great metropolis of Bournemouth designated one), but there's no logical reason why it should be sacrosanct. Ideally, expand communities near a railway station.
* As a test, look at where industries have closed where you live. Do the sites have housing on? The main undeveloped sites in towns are the ones that need a lot of decontamination (as City were willing to do with the Clayton Aniline site with its purple soil...)
I get a bit cross with people on the edge of green belt with a massive land take for their large house with a big garden, and a double garage not used for any of the four cars, who insist that everyone else should live in high-density housing in urban centres.