External rendering ? Is this what you are hacking off,? Then you refer to damp inside,yes cavity filled walls if the cause a breech in the cavity and allow moisture to cross over then the will create dampness inside, best thing for external ,hack off, apply an sbr coat 2/1 with cement ,then another coat, scratch with sand cement 5/1 with waterproofer ,a week later float it with 6/1/1 sand cement and lime. I am not an expert re the insulation, someone else will advise more on this