The width issue is kind of irrelevant. It may not be up to modern standards, but there is always a degree of flexibility and it being different to how they would do it now doesn't make it wrong.

You seem to be saying that the footpath surface has dropped about 5cm? That's a very long way and can't be put down to it wearing; it must have dropped, possibly due to an insufficient sub base or water leak below.

By all means try the Council again and try your Councillor (particularly if they are a member of the same party that controls the Council). However, it's their footpath that they allow you to drive over. Unless you have some kind of easement with specific repairing obligations, you will be right at the bottom of their priorities. You can thank more than a decade of 'austerity' for that. I imagine the suggestion you had was that you could get it done under a S.278 Agreement if you wanted to get to the top of the queue, but that would require you to pay.

Your council will have it on a cyclical maintenance schedule. They will probably tell you when it's due to be repaid. If not, you can put in a FOI request.

In any case, it won't be for ages. If it's causing you a problem, you might be better off with £30 worth of tarmac repair from B&Q and a shovel