I bet you could count the number of girlfriends and boyfriends who have paid off their partner's tax bills on one hand.
Just because he has a few quid, doesn't mean he should pay it. Her debt, her problem.
Of course you wouldn't pay the bill of a casual boyfriend or girlfriend. This is different though, even though they are not married, they are in a serious committed relationship and have children together. In these circumstances he should pay in my view.
I believe most couples in committed relationships do try to help each other out if they financially able to do so.