According to The Place Names Of Wiltshire (English Place-Name Society Volume XVI) by J.E.B. Gover, Allen Mawer and F.M. Stenton, published by Cambridge University Press, 1970:
Warminster. Brick Hill is Brickhill 1615 (Documents in the possession of the Marquess of Bath at Longleat House). Cf. Brickkiln Copse supra 36.