A lot of the people I see in my work (in a secure mental health facility) have been homeless or continue to be homeless often as a result of the complicated interplay of drug abuse, psychosis and the chaos of their own lives. It takes a 24 hour team of round the clock people to keep everyone safe - and even then there are occasions when things go very south very fast. Homelessness is a huge problem but I'm not convinced we can solve it very easily - and migrants who do arrive will also become homeless too, they show up in the hospital too, often dealing with psychosis and trauma brought about by wars and hardships they've endured to get here.
I think we should be putting the burden of housing onto large corporations. Big employers like the NHS, Supermarkets and Amazon should be offering subsidised housing as part of a package to their employees. This is also a Victorian idea (think of Bourneville) though it is less aggressive than the workhouses of the poor. We should also have a huge tax on second properties owned by those abroad. Very easy to blame penniless migrants, but much of the London housing is eaten up by the Arabs, Chinese and Russian second homes and luxury flats. If you want to take a house away from a UK resident and you don't intend to live in it full time, then you should pay at least 90% tax on the value of it per year. That would make it a less attractive house to own and lower the cost of housing for the rest of us.
There are many solutions to the housing crisis and homelessness but we must be wary of letting the political right convince us that the issue is with asylum seekers and a lack of money. There's plenty of money - just none of it is going to the right places.