So build up. Here in London people don't build up, for some reason (I mean other than office spaces, obviously). I think it's this nefarious british mentality that old is good. So you never demolish any 2 story buildings, you just build more outwards. Then you complain that the prices are insane.
The main problem is the greenbelt.
See, there we go again. Why is the problem the greenbelt? Between central London and the greenbelt there's a mind-blowing extension of small houses in every direction. There is A LOT that could be built before getting to the greenbelt. The greenbelt is only a problem if you want to continue building small houses.
Reminds me of this excellent documentary I saw on those millionaires who dig down instead of building up in London :P
In San Francisco there is a lot of progress that can be made without building up. For example, building more Accessory Dwelling Units [1] and subdividing oversized streets [2].