We put up a boundary fence on either side of our garden 17 years ago. One of the fences has now fallen down. The neighbour has put a note through the door saying it needs replacing, but I don’t see why we should pay for it if they’re not prepared to chip in.
It’s possible your title deeds plan will show which fence, if any, you are responsible for by marking it with arrows. It’s unlikely that you’re responsible for maintaining both sides. If your title deeds don’t mention fences at all then in all probability neither you nor your neighbours are responsible for maintaining the fences, and you don’t have to replace them. If you both want a fence you will have to reach agreement over the cost between you.