Oh, Pumpkin ... how frustrating & stressful.
He loves the fact he gets away with it, he rubs it in my face and doesn’t see them either so he literally gets to walk away without any responsibility even financially.
The thing is, you can take the sensible suggestions upthread & ring back to get a more helpful explanation. But you can also take a step back from the immediate pressure, & consider what you are going to gain through choosing to pursue it or drop it.
If you pursue, & manage to squeeze the £7/week, & that at least gives you a few handy quid (I know!) as well as the satisfaction of making him do the right thing.
However - are you also responding to the fact that he rubs his deliberate fuckwittery in your face? Because the other option is to simply disengage, so that he doesn't get to do that to you any more. As he doesn't bother to see his kids anyway, you could decide to throw the towel in over any financial contribution to him, ever - but your gain is never having to see him or deal with him.
Maybe the worse problem isn't losing the £7 bloody quid he's too tight to bestow upon his children. Maybe it's having him in your life at all. How happy would it make you to never have to deal with the git again?
Because - He thinks he is right, he doesn’t think he should pay for kids he doesn’t see. Great. Prove him right. Get it in writing, & make it happen. If you are able to do that, you gain all the satisfaction of him losing any hold over you whatsoever. And you'd also have a written guarantee that he's not going to be bothering you or the kids ever again.
Am sure there are more experienced pp who will be able to comment on the practicalities of either option. Sounds to be like you'd be better off just not having to think about him - but only you can weight that one up.
Good luck :)