Yes in theory but ... large private housebuilders buy up land and bank it, leaving it unbuilt to restrict supply and prevent competitors building. This drives up house prices without having to do anything.
Government likes using house prices as a measurement as to how well the economy is doing so they don't want to see house prices fall.
Building a shit load of houses to make them more affordable isn't in the interest of builders or government.

Does that include the thirteen overseas players in the Manchester United squad?