The temptation here is obviously to take this to mean Bridgwater in Somerset, some twenty miles west of Bruton, as most of the British texts were found in Somerset or Hampshire not very far away. However one version was found in Hertfordshire where there are lots of Bridgewater connections, the Earldom of Bridgewater originating here.
Source B5 Vaughan Williams Ms 8vo E 5, VWML; printed in Everyman's Book of English Country Songs, p.111
I don't know whether the 'version found in Hertfordshire' was really the one collected by Vaughan Williams in Herefordshire.