Letting agent claims fence is mine, not theirs?

the_lunatic_is_in_my_head

Hello OP

Fence usually belongs to who paid for it, deeds may say who is responsible for maintaining the boundary but that can be done with sticks and string. 

Occasionally they may state a fence or similar is to be maintained.

Without the deeds stating there must be a fence, even if the old fence belonged to the landlord they unlikely have any obligation to repair or replace, other than a desire to keep their tenants happy. 

If you need a fence to keep dogs in then it’s best to sort something to keep them in, otherwise it’s probably between your neighbour and their landlord.