Fence preventing maintenance

There are a couple of issues that I’m looking for advice on.

The entrance from Vicarage Road in to Kings Head Lane park borders the side of my house. My understanding is that the chain link fence is the council’s and the wall on the inside of it is the boundary of my property. There is a large amount of shrubbery, trees and ivy growing between the fence and the wall which is placing stress on the wall risking making it unsafe. I’m not completely sure whether it is council land or not but I’m fairly sure the chain link fence is owned by the council and it needs to be moved to gain access to the plants so they can be cut right back. What is the process for this? Can I request for the fence to be temporarily removed? I have sought advice from a builder and there is evidence of the wall being under stress from the weight and roots of the greenery. The risk of not taking action is that the wall will become unstable and potentially dangerous.

At the end of the garden is a tree in the park and my boundary wall has been declared unstable most likely because of the tree. I am looking to replace the wall but that will require workmen accessing it from the park, I’m not sure if there are any permissions required to undertake this work. Please can you confirm?