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)
You can put limits on rent increases through many means. For example limiting the increases per year, and limiting increases to when the landlord actually improves the building (with concent of the occupants). You can put taxes on landlords, you can ban things like AirBNB. You can make many areas nice to live in. You can construct affordable housing. You can make it almost impossible for landlords to evict tenants. There's lots of other ways that are used too.
Why would they? Would people in general be "earning" more money from basic income than current benefits? I mean you can't increase rent past the point people are able to pay.
It would probably drive some up and some down. People who have very little money have no bargaining power so they must pay what the landlord demands even for substandard accommodation. Such accommodation would probably go down in price if a basic income were instituted at a reasonable level (high enough for a reasonable life rather than just enough to avoid starvation) because people would be able to afford something a little better. This of course would drive the price of the bottom end of the good accommodation up. But the equilibrium would probably be at a point that was more comfortable for the tenants and landlords would have to work harder to attract them.
> I mean you can't increase rent past the point people are able to pay.
You can increase them past the point that people on lower wages/basic income can pay, driving them out of desirable or semi desirable areas to cheaper areas. See London as an example.
But I don't see why you need to live in London? You might like it and want to live there, but then you need the money to be able to.
Like I could move to Helsinki if I wanted to on my current salary, but I see no reason to do so. I live in smaller city (or maybe it's even considered a town) and I have plenty of extra money left over after my rent.
I don't need to nor, personally, want to. However, the people already there have a right to be there, especially those born in London, who grew up there, who have families, jobs, community involvement etc.
Yeah but that already happens with the current system; the worst case scenario is that nothing changes and people on lower wages keep being pushed out from more desirable areas.