Before departure all doors were checked closed and the associated warning lights were out. When the aircraft reached 4,000 ft. during a test flight for Certificate of Airworthiness renewal, the aircraft was depressurised and No.4 engine shut down. The rear passenger door, and rear galley door, warning lights then came on. This caused no undue concern because it had been experienced on several previous occasions when aircraft were being flown de-pressurised. After a three-engined climb to 12,000 ft., No.4 engine was re-started and the climb continued to 20,000 ft., while further tests were carried out. A descent to 15,000 ft . was then initiated, during which pressurisation of the cabin was started. When the cabin differential reached 1 Ib./sq.incb, the rear galley door warning light went out, but that for the passenger door remained on. On reaching 15,000 ft., the cabin differential 12 lb/sq inch, and it was maintained at that level while an inspection of the passenger door was made. It was then noticed that the door was about 1/4 inch from the fully closed position (to open, it has to be lifted over 2 inch). De-pressurisation and a further descent to 10,000 ft. were started so that the door could be closed properly. At about 12,000 ft., while the cabin was being de-pressurised and the aircraft was still descending, a heavy “thump” was heard and a pressure wave felt. The passenger door had fallen from the aircraft and further inspection showed that it had struck No.1 engine nacelle and had damaged the port wing boundary fence. Although there was no apparent malfunction, No.1 engine was shut down as a precautionary measure, and the aircraft then returned to London (Heathrow) without further incident.