During preparations for takeoff the flight crew were made aware that smoke could be seen emanating from the rear of the aircraft around the APU. The commander initiated a precautionary disembarkation and the APU, which had been running, shut itself down. It was apparent that the tail cone of the aircraft had become very hot, resulting in discolouration of the external surfaces. It was subsequently found that the APU exhaust duct liner had partially disintegrated, resulting in hot exhaust gases being directed outside the liner. Two days prior to this event, a piece of the liner had been ejected from the APU exhaust whilst the aircraft was on stand at Birmingham. However it was incorrectly identified as originating from an airport vehicle and the aircraft was allowed to continue in service.