So he works and doesn’t always pay?
And so to sweeten the deal you decided to just charge him rent, which he’s still not paying?
Honestly I would tell him to leave and go live on his zero contribution somewhere else.
You don’t have to end the relationship. Just stop bankrolling him. Bills should be the first thing he pays out when he gets paid. Not pay for crap and scrimp together what’s left, if anything.
You will save 25% for starters cos of council tax reduction. Child support - you would have to go through official channels as if he cannot pay towards his child now, well 🤣
You might also be eligible for other help, including towards childcare.
So ask yourself, what can he bring that you cannot do yourself, with him still living there?
Live apart, maintain a relationship if you want (and doesn’t include you cooking for him on a regular basis and doing his washing etc), and once he demonstrates he can be a responsible adult, partner and parent, the living apart thing can be reviewed.
And during his periods of unemployment, wasn’t he getting JSA? Although I do agree when earnings decrease the other person does support more financially. But once money returns to normal, so does their share of household expenses.
And whatever you do, until long term he has shown he has changed, don’t have any more financial ties. He will drag you down.