Damp is always a tricky problem. It might need to be Major Works. This means it is more than just a little patch up.
The Council will need to liaise with the neighbours. They will need to take off the plaster in the damp patch to find the problem. Presumably your neighbour also has a damp patch?
Depending on what they find affects what they do next. Ways to fix damp can be controversial, so I would also ask for a second opinion on any proposed solution before it happens. One size does not fit all.
After any fixes, the area will need to dry out. Finally, they will need to replaster and repaint the affected area and make good any other things affected (e.g. skirting board). Also note modern materials don’t always work well in old buildings.
Keep us posted!