I think, from a re-read, that it's an interior wall adjoining the ex-party wall that's now retaining. So it's safe to assume that ex-party wall is very wet, and the moisture is wicking from it along this adjoining interior wall.
A DPC isn't going to help. It may even make things worse by stopping it moving down, trapping it within the wall.
A DPC isn't going to help. It may even make things worse by stopping it moving down, trapping it within the wall.

