Oh like they have not thought of that.... yes that is highly sarcastic!
Builders would not touch affordable housing with a 10 mile pole even with tax incentives... not when they can earn a fortune building "normal" and luxury homes that are hella expensive. The government would have to fund it. And it is not just a UK problem btw, far from it.
As for spaces.. well that is when you get into problems, both space wise and zoning wise. Like it or not, councils want families that work, so building permits are targeted for such homes and not single person homes. It is a common problem world wide in cities and communities.. where people tend to live more and more alone, the zoning laws and regulations ban building single room apartments which pushes up prices massively for the existing ones.
Sure they could build a new community China style in the middle of no where and move people there, but that would require roads, public transport and so on as well, since relying on a car is not something you can when your monthly disposable income is a hundred pounds or two. Because if you cant provide these things.. how would the people in question be able to get to the jobs you want them to take?
Basically it is not simple at all and the only way to really get affordable homes built is by going through the government building option, but even that is against 30 years of policy in most countries. You see the UK has for the last many decades sold its affordable housing to the tenants in an attempt to get out of the business of providing homes. Problem is that they have not anticipated a growing population and changing family structure which results in a far greater need for 1 bedroom homes than 3 bedroom homes. This means couples or single people have been living in homes with a spare room because there is no alternative, and then comes this bedroom tax (provided they are on housing benefit) and it punishes them for having an extra room but does not provide them with any alternative other than renting the room out.. which in many cases is illegal (sub-let rules and all that crap) and frankly few people other than students would want to live in such a situation.. no bathroom you can call your own, having to share a kitchen and entrance with strangers.
It is not an easy situation, but the whole issue is that Cameron in all his stupidity with this policy has pushed 50+k homes into being behind on their rents and to potential homelessness, all to save a few bucks here and there.. because the actual saving from this policy is absolutely minimum relatively speaking. It is not like they will actually be saving anything if these 50k+ people are evicted, because many of them have children and then comes emergency housing which is always more expensive and all that crap.. not to mention the administrative headache it is causing.
No this is a very very bad policy that creates far far far more problems than it even remotely was suppose to solve.