Interior wall paint

Filey

Can anyone suggest a paint type for interior walls that isn't emulsion. My very old house has solid stone and rubble walls which have previously had an external cement render applied. No doubt when it was first built a lime mortar was used which would allow the walls to 'breathe', but someone has modernised it with impermeable cement render which means any damp now goes up instead of out into the atmosphere.

Parts of the internal walls downstairs being damp, they have trouble keeping the emulsion paint on the plaster, so I want to repaint with a breathable non emulsion non plasticky paint. Other than distemper, what can anyone suggest.

Maybe distemper is different now but when I was a child I remember the surface was very powdery and quite easy to rub off.
How about chalk paint? Milk paint? Anything else?