we know that the homeless and lack of housing is a huge problem here
I'm never so sure of that, the amount of services for homelessness seems disproportional to the number of homeless people. The NHS, Council and numerous charities exist for homelessness but what is the size of the problem?
Trying to look at figures around 2018 and 2019 (pre-Covid as the rules and funding changed temporarily) doesn't show a big problem.
Estimates for rough-sleeping for 2019 was 6 (on any day).
In 2019 households in temporary accommodation by the council were 29 (on one specific day).
Admittedly this can be looked on as the system is successful, a lot of people are given advice and limited help to prevent future/anticipated homelessness. On the other hand there will always be a turnaround, people leave housing for various reasons, a significant proportion of turnover is because the landlord/owner are not happy with the way the tenants/guests have behaved.