Really good article by Samuel Brittain in the FT on 19th June supporting building on a small part of the greenbelt
He also referenced a comment by Prof Paul Cheshire in the London School of Economics journal Centrepiece that more of the county of Surrey is devoted to golf courses than houses. Just 10 per cent of England is built up, and gardens cover nearly half of that area. Meanwhile a child in inner London derives no benefit from the existence of greenbelt land several miles away.
And I would add to that that this London child and their family both in the short and longer terms would benefit from increasing housing supply.