Though not about Westbury in particular this post on the Wiltshire History blog is worth reading in conjunction with Maxi's links.
http://www.wshc.eu/blog/Living-At-The-Workhouse-In-Secret-.htmlThe first workhouse in the area was at Westbury Leigh and the Westbury Union Workhouse was built on a previous older workhouse at what was Gooselands about 1835.
http://www.british-history.ac.uk/report.aspx?compid=16106There is a fascinating web site on Workhouses:
http://www.workhouses.org.uk/