my son suffered from noise from an adjoining flat, and after putting up with it for a while, he eventually went and knocked and very politely asked them to turn the music/tv down as it was causing him and other neighbours a problem. although they apologised and turned it down, he had to go back 2 or 3 times until they finally seemed to get the message that living in flats you have to be very sensitive to noise nuisance, and he's not had any bother since. if you read up about how to handle these situations, it recommends that you go and knock at a time when there's no actual noise happening and you're not seething, so you can have non-agressive conversation about it. and be polite but firm at all times.
if you have a residents committee, get involved with them. if the noise has been a nuisance to you, chances are someone else has heard it too. a letter put through the door reminding all tennant about noise nuisance 'from the residents committee' has a bit more clout than one person.
it wasn't a pop group though, just a couple of lads who hadn't even thought about anyone else being affected by their music/tv.