Sound blocking is largely proportional to the weight of the barrier. A continuous barrier with no gaps is essential as noise comes through gaps.
I've found old lime plaster on laths very effective, because it is not only thick, but also heavy.
Replacing old ceilings with ordinary plasterboard, which is both thinner and lighter, is noticeably less effective. Two layers plus skim are not too bad. The soundproofing plasterboard is extra-heavy.
On a wall you can use sand and cement render, which is quite easy to work with even if you are no expert, also cheap and easy to knock up. My old dad was no good as a plasterer, so he used S&C with a hard plaster skim. I now live in an area where it is found as the standard method in many houses, including my own, from initial build. Older ones have a lime and sand render plus skim.
For you, easiest would be to patch up the original lime. You can re-bond loose patches by injecting PVA adhesive behind it then pressing flat with a board.
Fill in any gaps. Interior brickwork in Victorian houses is usually very shoddy, because it was intended to be hidden with plaster. The gaps will be unfilled between floor and ceiling, behind skirting, and inside cupboards.
