That's not strictly true, bayliss - ownership of the fence (or any boundary eg a wall) depends on what the title deeds say. In the Q mentioned below, PostDog refers to a very useful site that you might want to have a look at
http://www.theanswerbank.co.uk/Law/Question535 169.html
If the council do own the fence you are referring to, then you need to contact them - if you are not sure, then contact them anyway to find this out.
The responsibility would be with the
owner of the land, not the tenant anyway.