Earlier quoted context omitted.
Unless you tax land. Nobody manufactures that for profit but profit handsomely from it they do.
Taxing land would increase rent and therefore increase food prices.
Demand for housing would remain the same.
Short term it would create a strong incentive not to hoard property. If it's not rented out it is losing money. Landlords would scramble to rent them out - driving up supply.
Medium term rents would decrease, too. A land tax would create a powerful incentive to yield low density housing in high value locations to be redeveloped into high density housing - increasing supply.
What would also go down is property prices. Significantly.
It would kill all political will to fight redevelopment too. There would be no point fighting to declare a launderette historic to prevent it from being turned into apartments. Desperation for local housing wouldnt get directly turned into home equity and higher rents like it does now, it would just jack up your tax bill.