You need to get over the myth that immigrants, legal or otherwise, get provided with housing. It's not true.
Only if/when someone gets an asylum request granted so they have refugee status can they can join social housing waiting lists, and then they're subject to the same qualification criteria as everybody else. Nobody is "put to the bottom" of the list to make way for anyone.
And illegal immigrants don't get "handouts when they hit the shore" at all, they have zero entitlement to benefits...
Illegal immigrants cannot claim benefits in the UK. A person is classed as an illegal immigrant when they do not have the right to remain in the country.
The UK government, in response to a petition urging it to “Stop all benefits to illegal immigrants completely”, said in 2015: “Illegal immigrants and failed asylum seekers are not entitled to, and do not get, benefits from the UK’s welfare system”.