Government price controls do not fundamentally change the cost only the price.
If the government is so efficient and can, somehow, make housing cheaper than it would be in a free market why shouldn't they also take control of the food supply? Computers? Software? All industry?
Because thus far they have intervened with the opposite effect, to push housing prices upwards.
In London this is through the Green Belt, torturous planning laws, height and density restrictions, low interest rates, government-backed mortgages and lending schemes, etc.
Supply in the markets for food, computers, software, etc. is not nearly so controlled by government action (or inaction).
The government created a market failure by passing restrictive zoning regulations leading to a severe under-supply of housing. Resolving the market failure requires either eliminating the restrictions or providing enough cash money to justify the builder's expense in contending with them.
Obviously the better solution is to do away with the restrictions, but politics is the devil's day job and all that.
Government policy determines the price of land. Land is a major component of the cost of housing, so it stands to reason that government intervention in housing policy can make housing less expensive.
For instance, imposing a very high land value tax would reduce the value of land, which would in turn reduce the cost of housing.
> For instance, imposing a very high land value tax would reduce the value of land, which would in turn reduce the cost of housing.
It would only potentially reduce the tax-exclusive cost of housing. It would not reduce the tax-inclusive cost. (In fact, the rational expectation would be that it would radically increase the tax-inclusive cost.)
It would not change the tax-inclusive cost of housing. Land taxes can not be passed on.
You are right, that the tax-inclusive cost of housing won't change with a land tax on its own, at least not as a first order effect.
If however, you eg use the land tax proceeds to lower taxes on labour and capital, building higher (ie using more capital for housing) will become more economically feasible. (No economic revenue will be lost. Lower taxes in a jurisdiction directly lead to higher land prices---which the land tax will capture.)
This is going off into the weeds, but the government can and does provide food assistance: food stamps. Still, though, people use those to purchase food at market prices, which makes sense.
