Once you’ve identified the moisture source you can go about rectifying the issue. This may require a builder or plumber if the problem is beyond your DIY skills. Your local damp specialists will also be able to take a look and suggest a course of action to cut off the moisture supply and prevent further water ingress.
Hold off on any repair works until the property has had a chance to dry out so you can see if there is any noticeable damage. You may want to get a professional opinion from TDT Preservation if you think there could be black mould growth or dry rot.
If you get the all clear then you can repair damaged plaster and repaint. If not then the black mould will need to be carefully removed and/or undergo timber rot treatment. Remember, the longer you leave a penetrating damp problem, the more expensive it is to repair.