Fence problem

TCPPC

Hi anyone experience a problem with your neighbour. Basically their fence connect to mine is falling over and pulling ours down. The only support is the 3 bins and our central post which sat on my land.

We need to fix ours, the landlord isn’t replying, if we ask a contractor to come out, can we ask them to cut theirs off from ours? But this way their side would surely fall. I feel it’s unfair on us needing to fix their side again and again in the future. Would I be liable if the landlord comes back saying I damaged their fence!

or should I wait until their side has fallen then do the work.