It's actual a council "law". They're in their right to do it.

As someone who has half a jungle that grows over our fence from our neighbours, into our carport and all over our damn car, I hate the fact i have to prune a tree thing that isn't mine. If I wanted to prune an out of control plant I'd plant my own. (ok, vent over XD) I think it's unfair to expect them to take the branches away.

It would have been nice of them to give you the heads up tho, I think.