I quite agree that Beachbum should take the honour with this one. The true origin of the name is lost in the mists of time, or a musty box in an archive store, but its later reuse of 'Jumping Downs' can be traced on the earlier maps of the Ordnance Survey from 1871, as well as the Barham Tithe map of 1842. There is the possibility it may have referred to quarrying of the moderately steep sloping valley sides as a portion of land opposite recorded as 'Part of Stone Quarry Field' and 'Stone Quarry Field'.
The two included images show it in recent years as a nature reserve, whilst the second is the LIDAR image showing the course of the motorcycle track, the lumps and bumps of which are vaguely discernible in the reserve today. For its O.S. location, its at TR19407 48639, or 51°11'41.52"N,001°08'19.83"E in watery terms.
Over to you Beachbum and apologies for the delays.