OG, there are firms that sell 'soundproof plasterboard' but it's basically the thicker gyproc thermal board ie it has a layer of rigid foreproof foam bonded to the back.
I can empathise with the OP - we too have a inter-war semi, and some of the original builder's bodges have to be seen. This includes a less-than-meaty party wall, and as the next doors have gone for hardwood floors, lots of sound penetration.
If we stay in this house I'll get round to it, but there are lots of similarities between heat insulation and sound deadening.
Are there lots of fixtures on your party wall? That would be a problem if so. If not, it's an annoying but simple job to pry off or unscrew the plasterboard, install sound-deadening insulation (oridnary stuff sold for lofts), reboard and re-plaster.
That is, provided the boards installed by the builder are onto battens. If stuck directly to the brick, it won't work.
You could stick a layer of gyproc thermal board over the existing, replaster etc but that's a real bodge n a half.