Someone once said that dealing with sound is rather like trying to contain water. It just seeps everywhere. Two completely different types of sound transmission need dealing with.
The first is - Airborne sound. Simply the sound you hear from next door, or even from the street, carried by air.
The other is - Impact sound. When someone bangs on the wall, or even any wall or floor connected to your party wall.
Sealing up gaps of course is obvious, but there's no substitute for "density". A thick, concrete wall is ideal, but not an option here. Ivor's link below is a good alternative though. That, combined with OG's cavity idea would be pretty good.
There are all kinds of soundproofing products around that can help to some extent, but a simpler option is to........
Make up a simple studwork wall and fix it 50mm away from the existing one. Fix it all around with flexible, rubber mountings. This will help reduce Impact sound transmission.
Fill the cavity and the studwork with "Rockwool" sound insulation.
Cover the stud wall with something like the one in Ivor's link, or, at lest one layer of "Gyproc Soundbloc" plasterboard. Two layers is a lot better. This will help to reduce Airborne sound.
Sounds like "a bit of a game", as they say down here in the Shires, but it's a simple DIY job. You don't have to plaster it if you don't want to.