basement tanked with membrane on walls but damp coming through the fire place

Does this look like salting, is the paint peeling away from the wall. If your chimney has been capped or is water tight it's probably salt contamination due to hygroscopic minerals from inside the chimney and not so mush damp. I would recommend injecting a cream DPC then a physical barrier, damp proof membrane then dot dab plaster board or a tanking slurry then sand cement mix 2plaster sand 1sharp sand to 1 bag cement with a salt inhibitor then skim finish.