No, rents stabilising along with the price of houses, and falling in real terms as incomes rise. Rents can’t just be jacked up by landlords at will or because their costs go up, demand falls away. Otherwise it would already have happened.
So if landlords face an increased cost – as some but not all by any means will, they could seek to recover by ramping rents but to the extent that tenants are already paying as much as they can, demand will simply drop.
I would expect the price of those properties to suffer to the extent that the landlord is then making at least the minimum deemed yield.