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A Cessna 172N Skyhawk aircraft was planned to fly from Birmingham to Edinburgh via Gamston, Ottringham, Newcastle and St Abb's Head. No problems were encountered during the flight north and the aircraft was transferred from Scottish radar to Edinburgh approach at 23.37 hrs as it turned at St Abbs. At 23.43 hrs the pilot reported level at 4,000 ft amsl and was advised that he had 26 track miles to touch‐down. During the next seven minutes Edinburgh gave the pilot two heading changes and then a descent to 3,000 ft amsl. As he was being given this descent clearance at 23.50 hrs, the pilot became aware of a change in the engine note; he activated the carburettor heat and checked the engine temperature and pressure gauges. The temperatures were normal, but the oil pressure indicated zero; the pilot reported this to Edinburgh and then stated that the engine was losing power.