If enough houses can be built, and basic income is high enough to pay free market prices, then any landlord who asks too high a price, will price themselves out of the market because there will be other cheaper houses. But for this it's vital that the supply of houses is unrestricted.
Of course a landlord might bait and switch with low rent as you move in, and rapidly increasing rent once you get settled. That's simply something that needs to be banned. After you've moved in, landlords should only be allowed to increase rent by either inflation, or the average increase in new rent in the area. But preferably just inflation.