I think you will probably see lower rents, when they remove the housing benefits. At least if housing benefits are implemented the same way as in Sweden. When I was a student, the state payed for the part of the rent that was between €300-€450. So when I chose which apartment I wanted, I obviously chose the more expensive one, since I had no incentive to do otherwise. The people to owned the student apartments eventually caught on, and raised the price of all student apartments to around €440. (not the exact numbers, just to illustrate the point)