Issues with damp in older properties often stem with modernisation not taking into account older building techniques - something developers are notorious for because these don't come out until people start living in the properties.
Particularly anything lime - which needs to breathe and move naturally.
Adding double glazing can be a major contributory factor, in older properties double glazing should always have trickle vents. Without them you won't have adequate ventilation. The other option of course is just to keep your windows constantly open a crack.
Penetrating/ rising damp is comparatively rare - 95% of the time it's a ventilation issue.
Or something as daft as washing being dried indoors.
If you have big problem walls on single skin the usual practise is to strip all plaster and render then dryline, which can sometimes help
Whatever you do, don't go slapping PVA on the walls. DIY programs on tv have spread massively wrong information about the usage of PVA - only time it should go near a wall is before plastering (to reduce porosity which will dry the plaster too quickly and cause a failure), never after plastering or as a problem solver, it'll create big problems down the line.
Fix damp problems, dry plaster, then paint with alkali resisting primer and decorate.