They can and do claim all benefits, as do the "accepted" refugees from Kabul/Afghanistan.
The problem in the South (and maybe elsewhere), is the lack of any housing, not lack of Housing Benefits.
Private landlords are becoming more reluctant to take on any tenants on benefits, social housing is full, and massive waiting lists, and house prices, to buy, are through the roof.
www.gov.uk/government/news/immediate-benefit-support-for-those-fleeing-the-invasion-in-ukraine
I am not a messy person but...
Happy Birthday - 100 years on Earth
