Have damp on my gable end wall due to condensation, can i insulate the inside walls?

If you have condensation you should deal with it by increasing ventilation especially in bathrooms and kitchen and reduce moisture produced by drying clothes inside etc. If you have damp ingress then ideally this should be dealt with from the outside by re-plastering with a correct material. If you want to increase insulation internally this will certainly help prevent condensation but you need to ensure that you completely seal the insulation to the walls or damp could migrate past it and into the wall where it could condense and cause structural problems. I would consider use of correct insulated plasterboard. Depending how this is fixed you do not need to let the walls fully dry. However if you have moisture ingress from outside you could have problems if the root cause is not addressed. I hope this helps. Ian