Egg boxes are a cheap and cheerful way of stopping sound from reflecting directly back from a hard surface but will do now't to stop most of the sound from passing straight through.

What you need to aim for is density and, as such, two brick walls are better than one! The problem you'll have in a semi or terraced property is that most of the sound you generate won't pass through the wall itself but will find its way through the floor and ceiling. Unfortunately, in the interests of cheapness, floor/ceiling joists tend to sit in holes in the party wall and often butt up to one another allowing sound to pass through the gaps.

Another thing to bear in mind is that if you're intending to carry out work to a party wall other than say re-plastering it, putting up cupboards or knocking nails in to hang pictures, you have various legal obligations under the "Party Wall Act". So upset your neighbours at your peril as it can be a costly business not complying with its requirements.