Suggestion (off the top of my head) - an incentive for people with a spare room (I wonder how many thousands of spare rooms Worthingtinians have ?) to allow a homeless person to stay for 4 weeks. Enough time to get washed, stabilise, and maybe engage with the jobcentre.
Are you fucking kidding me??? You are coming across as extremely naive. The vast majority of long term homeless don't manage in supported accommodation. PMSL that you think the problem is a lack of beds and that people with spare rooms should open up their houses for '4 weeks' and that will 'stabilise' the life of someone who is homeless.
I have spent a lot of time voukenteering with a charity in the homeless space. Lack of a roof isn't the key issue - being able to manage a tenancy whilst having poor MH or substance addiction are the key issues. It's incredibly demoralising to work hard to get someone onto a supported tenancy - better than a hostel, their own flat with lots and lots of support to help them on the path to moving onto being more self supporting. And then about 3 weeks after they've got the supported tenancy, they are back on the streets because they couldn't cope.
And whilst this is something close to my heart there is no fucking way i would let any of the clients I worked with into my home!