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"Homeless" in that sense, however, are not rough sleepers (people who actually sleep outside), which would seem to be what is meant in this context.

It's by no means zero, but in autum 2024, rough sleepers were estimated at less than 4700 in the UK. That might well represent and undercount, but it is certainly nowhere remotely near the people counted as homeless, who would include anyone without a permanent address, such a people e.g. sleeping at friends places on a non-permnanet basis.