The UK's problems are about distribution not supply. We subsidise OAPs to sit alone in 4 bed houses in areas that need workers, then there is no space or money left for working families...
This is true in more than just the UK. It's also not simply old people living in oversized houses. Think holiday homes, AirBnB, second homes, land-banked properties, etc.
Any government that truly wanted to address it's accommodation crisis should start by conducting a thorough survey of residences and determine how many are actually being used as a primary residence.