The only light machine gun that I'm aware of that fits this general description is/was the BESAL, a proposed replacement for the BREN when Enfield was in danger of being bombed out of business by the Germans; of course, that was in .303, not 7.62x39. If you can post a picture, especially of any of the markings at all, we could probably let you know in no time.
Edit: here's a scan of the only picture of the BESAL I could find, showing the cocking handle built into the pistol-grip: