Also in Mr Britton's 1801 'Beauties of Wilshire' it's mentioned that Alfred's Tower "was erected [in 1772) by Mr. Henry Hoare, to commemorate a signal victory which Alfred obtained over the Danes near this spot... Tradition (which has commonly some foundation for its stories) says that there was so much blood shed in the above-mentioned battle, that the water was stained therewith three leagues below Christ-church."
And to link the King Alfred and the beacon stories together (see misc. post), the website devoted to the tower quotes Harper's Weekly from 1901: "Local tradition says that on Stourton hill... the beacon was lighted that summoned the men of three counties to Alfred's standard."
The site also suggests that the boundaries of those three counties (Wiltshire, Somerset and Dorset) once met up here. Probably.