Our council is responsible for the trees on the street and they cut them around power lines. I also got them to trim one of their trees that was overhanging our front steps. They came and trimmed it the next week after I reported it. It does depend on the local by-laws but generally if the tree is on concil land it is council property and therefore their problem. If it was reversed (ie your tree overhanging their land) you would be resonsible for pruning it.