£1000 a month for a single person certainly sounds like poverty, but £2000 a month for a couple sounds more manageable. If they each find a side gig that pays just another £100 a week, they're suddenly into the top half of households [0] - even better than that outside London.
That's in line with the OP's point that it's not really affordable compared with the current system, for all that system's flaws
The fact that a UBI which set at a rate low enough to make some existing benefit dependents would also be a generous subsidy to homeowning couples who might be able to use it to to retire a decade or two early isn't one of its strong points
[0] https://www.ons.gov.uk/peoplepopulationandcommunity/personal...