Overhanging tree

I have attached a photo showing the location of the dish to the tree. I am not able to move the dish as it needs to be fixed to my flat.
I originally just asked the council for permission for ME to pay MY OWN MONEY a tree surgeon to cut the tree back. They ignored this saying they do not cut back treed for this reason.. blah blah blah. Avoiding what I asked.
After being passed from department to department I just got nowhere. I then noticed the tree is overhanging the footpath and over the boundary to the block of flats.
Now it gets complicated. .. I rent the flat from the council... so I'm not sure where I stand legally in getting the tree cut back. I know if I owned the land I have every legal right to get the branches cut back.
I do however pay maintenance in my rent for the ground the tree is overhanging.
Can anyone help please?
I also know there is no TPO on the tree and there is CLEAR evidence that branches have been removed in the past. So why they say they only cut back trees if there is danger to life or property I don't know.
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Can you get Virgin Cable instead?
Relocating the dish is also out of the question as some of the flats are privately owned.
There are black marks on the trunk where branches have been removed previously. I seriously doubt they were causing danger or damage either.
Bit sad really but the council finally got back to me today, exactly 12 months after I first contacted them.
He couldn' give a reason why but the whole tree is coming down and the stump ground down.
I would have preferred just a few branches to be pruned back, but they must be doing it for another reason.
Plus many branches had been removed in the past.
Thanks for the replies anyway. 👍