We have repointing booked in for a few weeks time so hopefully will make some difference. The damp is coming up from the floor of the fireplace not the walls as that’s what we originally thought.Your brickwork badly needs repointing as it will speed rain penetration as it is.
Damp in fireplace will be from chimney, either not capped and ventilated and / or problems at roof level .You don’t have rising damp .
Probably should have mentioned that we’ve had damp on every wall of the ground floor including internal walls. Had a membrane put on before the new plaster to stop it coming through but obviously the root cause is still causing us grief.