Note that the UK already has a system of housing benefit which covers (most of) the cost of accomodation for people on low incomes. That may be a separate issue.
Housing benefits would have to be eliminated to make UBI viable cost-wise -- and indeed that is one of the biggest reasons why UBI or negative income tax as a replacement to benefits is politically unpopular.
While UBI would be more efficient (everybody gets a minimum amount of money that they can use towards housing or whatever else), that would mean HUGE losses among the welfare recipients in expensive places -- in London, housing benefit (LHA) can amount to $18k a year for a small family or $30k a year for a big one, and UBI will not fully replace that. The laments about social cleansing will be loud.
While UBI would be more efficient (everybody gets a minimum amount of money that they can use towards housing or whatever else), that would mean HUGE losses among the welfare recipients in expensive places -- in London, housing benefit (LHA) can amount to $18k a year for a small family or $30k a year for a big one, and UBI will not fully replace that. The laments about social cleansing will be loud.