You want a cheapish bodge? Go to B&Q and look at their cheap cladding - 7.5mm tongue and groove planks at around £2.50 for a square metre.
Buy enough of those to go over the walls you share with the neighbours, get some 2x2 battens on which to stick 'em, and between the cladding and the wall put some insulation - polystyrene sheeting's good for soundproofing but lethal as a fire risk, but glass wool/rockwool is pretty good too.
You do lose some of the overall size of the room, but it should prevent the neighbours from killing you!
You can also buy special anechoic foam from the more upmarket, anally-retentive hi-fi stores, but it's bloody ugly, attracts dust and makes you think you're living in a room lined with black tripe.