Could Green-Belt Land Help the Economy?

Anecdotally, I get the impression that there are lots of people who would like to buy a house if only they could afford it. So, how about allowing new houses to be built on green-belt land? Here are some calculations:

There are 22.3 million dwellings in England. There are also 1.64 million hectares of England defined as green-belt land. According to this document from the government (pdf), houses should be built at a density of between 30 and 50 houses per hectare. Let's take 40. In order to increase England's stock of houses by 10% (2.2 million) we would need 55,000 hectares. That's about 3.4% of current green-belt land and about 0.4% of the entire land surface of England.

Without thinking about this too deeply it seems to me that doing this would have the following benefits:
1) Increase growth
2) Reduce inflation
3) Reduce unemployment
4) Costs nothing (possibly raises revenue)

The costs are that house prices fall. Well, that could be a good thing in the long run couldn't it? Of course people who already own a house or have a mortgage lose out but it's for the greater long-term good of everyone in the country. Or have I missed something?

NB: I've used figures for England only because they were the easiest to find.

Thanks to Tim Worstall for getting me thinking about this point.