Some 19-year-old men can eat a lot, use quite a bit of leccy and gas if they came a lot and/or take long showers or baths, there's his washing to consider. There's a reason why people qualify for child benefit, after all
He'll have to accept that food might be a bit less for a while, he can't game constantly and he's only allowed quick showers. He has to give and take too.
'Signing on' is now UC. There is a wait of at least 5 weeks for any money unless you borrow against it, which you'll have to pay back, thereby reducing your benefit later on, and he'll need to show he's spent 35 hours a week online looking for work. He needs a computer or phone to use for that and transport to and from the Job Centre (if he can't walk to it) and to any work placements.
Everyone that is out of work has to do this too, why should he be any different? The job centre have phones & computers to use, as does the library. He's going to have to put himself out in all of this too. He could look for a cheap bike on ebay or freecycle if the job centre is a little bit further away. If UC doesn't kick in for 5 weeks and he hasn't got any work in that time maybe he could register with a GP there and tell them the situation and see if they will refer him to a food bank so he can bring some food in that way.
If you are on the breadline already, it's a big thing to take on another adult.
It would only be temporary, and if not, if he doesn't get a job then he's had his chance and OP will be within her rights to tell him to leave.