I seem to recall that the dropped kerb has to be as wide as the driveway or opening it is leading to.
If you create, or widen, an entrance then you must have a dropped kerb in place of equal width. It gets a bit complicated if you have lamposts or other street furniture there as you have to pay for those to be moved as well.
You can arrange for the work to be done yourself, you need to apply to the council for a permit/licence so they can come out and tell you what needs to be done, and then arrange for/pay for the work by an approved contractor (the council can give you a list), or you can get them to do it.
If you do the work yourself, or use a non approved contractor, then they can rip it all out, do the work again, and bill you for it. If you use blocks of wood etc to bump up the kerb they can remove them, and bill you for doing so.
From your message it seems like they told him to do it but then did it themselves a few days later. If they gave him time but nothing was done, then they acted correctly.
The only get out you might have is that the widening was done five years ago, but the legal challenge to that would probably cost more than the bill.
If he doesn't pay they'll probably apply for (and get) an "interest" in the property, which would mean that the bill would be paid if/when the house was sold. This would show in any searches and could make getting a loan or remortgage on it more difficult.
Try talking to them, plead ignorance, and make an offer (depending on the amount of work these jobs usually cost £400 - £650 with contractors). You might have more luck with this if they gave you very little time between sending you a letter to notify it needed to be done and them coming out and doing it.