This is so far out of line I don't know where to begin.
He lives in your house, wherever he lives he will have to pay rent and bills, regardless of who has the mortgage. That is not negotiable, it is the way it is. If he moved out somewhere else (which by the way I would insist on) his overheads are going to be far higher.
He either thinks this is fair, in which case he lacks any basic intelligence or he is taking the piss out of you.
This is not about him supporting you financially, if you put it like that then he would likely think it is unreasonable (it isn't, but he might take that position), this is about him paying his way.
This is about him paying for his share of the bills (at the very very least 30-40% as there is 3 of you but really I feel 50% is fair) and paying his share of the rent/mortgage which I would ask for the going rate on, so whatever he would have to pay locally in a flat share he should pay to you.
If he refuses to pay his share I don't see that you will ever respect him, you will grow to resent him more and eventually it will break up the relationship. But he'll be ok, he'll have squirrelled away thousands of pounds he never paid for his upkeep. You on the other hand will likely be stuck with debts.
Lay down the law, for the good of the relationship.