Our deeds also explicitly say “joint” responsibility for the fences.
We needed a new fence on one 15m stretch with a neighbour.
In practice it means you need to consult them if you want to replace the fence which you should do anyway.
If you both agree it needs replaced, technically they should pay half. However if you want something more expensive than they imagine, you might have to pay the uplift.
I suppose if you don’t get on you could put the new fence on your side of the boundary leaving the original. But thats not going to improve relations.
In our case I bought everything, I spent two weekends diggging holes and installing the fence myself. My neighbour payed half for the materials.
Basically if you want a new fence, be prepared to pay for it yourself, and see your neighbour paying half as a bonus. Equally your neighbour might decide to replace a fence that in your opinion is perfectly fine and ask you to pay half…..