Reducing demand by reducing immigration will absolutely reduce house prices. That is the very basis of supply and demand.
Removing all immigrants that have overstayed their visa is a no-brainer. Reducing immigration to a sustainable level is another. Anyone disagreeing doesn’t actually want to fix the housing crisis.
The government doesn’t build houses. Taxpayer dollars don’t build houses.
I agree the submarine deal is ridiculous, we don’t need submarines - but the money paying for them wouldn’t be used to build houses or address the housing crisis.