Any decision to build on the green belt is going to be controversial. There is a clear need to increase supply of all types of home however, and no appetite for creating any new towns any time soon. The answer is either to build up or build out. 

The Centre for Cities has released interesting research (and another cool map) showing that just 5.2% of existing green belt around the ten least affordable cities in the UK would need to be sacrificed to allow construction of 1.5 million new homes.