Obviously, I don't know anything about his particular circumstances, but how much does it cost to rent a room in a shared house/flat in London? Round my way, for somewhere decent, you need to spend around £400 a month, I guess, but it's probably more in London. A friend of mine works as a labourer on a contract by contract basis, so he has periods when he is out of work, but he does rent a room. It's not ideal, but it must be a better option than a hostel, by the sounds of what he is saying. He has a job so will be able to get a reference from work and has regular earnings, even if it's zero hours.
And before you all throw your hands in the air and shout Tory! I am just trying understand why that is not a better option for this man.