This has happened to our wall 🙁
A damp meter reading didnt show anything but the house started to smell a bit musty.
After a bit of investigation found out that it is a solid wall (I assumed it was cavity as the house is 1950s) and that when the neighbours built their extension their builders broke our guttering off which is very hard for us to see due to the position of our house and their new extension.
So water was pouring straight out of the gutters onto the wall and coming through.
The gutter has since been fixed and the musty smell slowly has disappeared, so I’m hoping soon to be able to repair the enormous discoloured bumpy patches on the wall!
So in your case it is likely to be water coming through the wall for some reason. If its gutters, the same as us, its not an expensive repair. But you should definitely find out what is causing it before deciding if you are happy to proceed or not.