The guy's been datastormed but there's an important point to dispute on this one
UK councils legally have to offer housing in the event that housing becomes impossible, like your rented property being sold off and being unable to afford a new place, thus you receive temp. accommodation, however in many cases true homelessness is a domestic/familial issue where for whatever reason a person has been kicked out of their home and potentially distanced or disowned. There is no safety net in-place for that, since they tend to genuinely have little to nothing and without any sort of permanent address it's a nightmare for the council to reach out to them.
There are also situations where people abuse the good hearts of others and become professional beggars, living comfortably and spending the days begging under a false pretense of being homeless. Those people undermine the actual struggles that many people face, like the poor trans person's genuine struggles mentioned before.
Its one where yeah, there are options out there, but it isnt always as available as one might think