This is the Manuel Burn, which has its source in the Blackbraes and flows to the River Avon at Manuel Mill farm, near the village of Whitecross.
Previously, I found a web site that described in graphic detail how the burn had impeded the retreat of troops who had been defeated in one of the battles in the area, but sadly I cannot find it any more. However, in searching for it I have read about a ruined nunnery, and this will definitely be something I shall be looking to explore in the near future.
This stretch, however, is pretty much exclusively used as dog-walking territory now!