Just wanted to clarify some points on agencies supporting homeless people who are not in the UK legally.
Homeless support charities do have to define the immigration status of their guests and most London based charities share a database of information about guests so they can be tracked through their interactions with different groups
If they are "no recourse to public funds" then no public service or charity recieving government or council funds can assist with accomodation etc. This is why some charities do have to check immigration status
Only charities that are entirely funded through public fundraising can provide accommodation. I volunteer for one of these types of charity.
There are only around 70-80 beds in the whole of London for people who are no recourse to public funds.
When temperatures are below freezing for more than 2 nights in a row, London's severe weather Emergency protocol (SWEP) comes into play and emergency beds (or at least mattresses on floor) are opened up and charities which take government funds are for a few days allowed to ignore the "no recourse" bit and can accomodate anyone.
But SWEP beds can be a collection of mats on the floor in the lounge of a more permanent shelter or even a sleeping bag on the floor of an empty room on a police station (not many people know that the police effectively run emergency homeless accomodation sometimes, it's not all stations though but genuinely a good place to ask for help in a crisis)
but SWEP is crowded, full of vulnerable people and quite a few homeless people would rather stay on the streets than go in there.
SWEP is in force at the moment, I think but I've not been volunteering for the last two weeks so I'm not 100pc certain.
Anyway the point I am making is that actually it's bloody hard for homeless people without the right to be here and yes, their immigration status is checked and recorded at various points and databased.
And about 50pc of our guests who are "no recourse to public funds" end up winning on appeal at immigration tribunals so the idea that we should just throw them out would mean throwing out lots of people who are actually here legally, it just takes time to prove it.
These are two broad groups (for our shelter)
Eritreans who get turned down for asylum almost always win on appeal. It's a stupid stupid inhumane government policy to reject them and then drag it out for a year with no funds until they inevitably win on appeal.
Older people from the Caribbean who came here a long time ago (in some cases before independence from the UK) and its legally complicated to sort out and prove but they are almost all legal eventually. In some cases they are actually British citizens depending on when and where they were born but have no paperwork. So it requires a lot of research and document requests by volunteer lawyers to fix.