No, I think such low density housing is actually the cause of the problem,

Wartime houses are not low density though, they're medium density. Many are higher density than modern townhouses due to their efficient use of space (small rooms, tiny yards, limited parking, narrow streets, etc). Now, can those efficiencies be applied to townhouses? Yes! For example, the old rowhouses in Philadelphia or terrace homes in London, and these are an even more efficient use of space than wartime houses.

And once again, I'm not agreeing with @rab that we need to build wartime housing en masse. However, as NJB points out, these kind of homes are very desirable and I think there is a place for some efficient SFHs in the solution to this problem.