I wish I could find my thread about my neighbours from hell a few years ago, oh god what an episode that was!! tried everything, never worked. Most nights their music was SO loud the neighbours on the OTHER side of the road could hear it. Police weren't interested and the council provide too much red tape to make it even worth attempting.
I know it's not an option for you, but in the end we found somewhere else and moved. Landlord came over and begged us to stay, said he's kick the neighbours out if we'd stay instead. Was too late by then though.
I say go softly softly first, you never know it might work. You always have the option to step it up later on if it doesn't work.