It sounds like the conversion has undermined how the original architect’s design acoustically separated the houses. So, the short answer to your question is essential that no, it’s not possible or cost effective to completely soundproof your house. However, it may be possible to reduce the problem. High-frequency noise, such as the scream of an electric saw, is carried through the air. The best defence against this is weight and there are several wall- and floor-lining products, which are essentially heavy-weight plasterboard, that can be used to help. You could even go to the extreme of building a whole new skin inside your party wall, but you would loose a lot of internal space. Low-frequency noise, such as the thump of someone’s boots is carried across structure, in your case via the joists, which share a party wall with your neighbours. The most effective way to reduce this noise is to physically break the chain of solid material along which the sound is travelling. One way of doing this is to expose the ends of the joists and one by one, cut them off, and re-support them to the wall with a joist hanger, which itself can be isolated acoustically from the wall. Both options are costly, but I know how disturbing noise can be and you may want to go to such lengths.