Get a job - any job that brings some money in will do.
A bit of volunteering can't lift the financial burden in the slightest. But a job, whether it's cleaning, a bit of admin, temping, whatever, will show you're making efforts to change your lives.
After all, if you refuse on whatever grounds, there's a good chance he'll leave and then you'll have no choice but to work, as Universal Credit won't let you get away with it.
DP was like that. He had anxiety/low self esteem and tried saying he'd be a house husband. Not good enough for me - I had to work to keep a roof over our heads, and I was on the point of saying I was done, as the mental and physical load of work, the bills, the housework and shit meals had got me to the brink of calling him a fucking cocklodger/sponge/leech and to piss off and find somebody else to live off.
Admittedly, this coincided with a bereavement and my impending redundancy, so I wasn't in the mindset to be particularly tactful anymore, so I think he was aware that I was just at my absolute limit. I think what actually got him to realise was an exhausted 'You know you'll have to get a job when I drop dead from a heart attack, don't you?', followed by my going to bed every night at 7pm.
But it had to get to that point for him to realise it was going to end things if he continued to sit back and leave me to do the grown up stuff.
He got some temping work. Then he got a job and the worry, stress and gut churning anxiety I had at 4am, knowing as soon as I left for work, he'd be asleep or pottering about online, lifted immediately.
And he's actually happier - he bought a much needed washing machine with his first pay and he seems quite proud of himself for doing that. It's an obvious symbol of him contributing, combined with getting up, making sure he has clean work clothes, dealing with people, etc.