> London still has large amounts of "brownfield" low-value industrial land as well as low-quality, low-density suburban housing that is often close to existing, under-used infrastructure. We are much better off making better use of that existing land to build walkable/cycle-able neighbourhoods that are well served by public transport.

It's not either/or. At the level of housing demand that London has, we need to build everywhere.

> Expanding into the greenbelt is just lazy development that would increase London's existing problems (car traffic, air quality, sprawl).

There's no reason building in the greenbelt would be worse for car traffic or air quality - indeed there are quite a few places where there's already a railway or underground station, but no houses get built because it's greenbelt.

> ... and there are plenty of small neighbourhood parks in London! I can't imagine that you're ever more than 5-10 minutes walk from one.

Clearly you've never been to Tottenham. (There was a "green" on paper, but it's just a square of grass next to a main road. The marshes are lovely if you can get out to them, but they weren't somewhere you could stop off on the way home from work).