The two places you mention are close to each other. Just a guess, but possibly Mr. Basset would have been a local landowner.
I spent 40 weeks stationed at RAF Compton Basset back in 1947 training to be a wop/tpo.
The suffix Bassett is the surname of the lords of the principal manor in the 12th and 13th centuries
Have a look at British History on Line http://www.british-history.ac.uk/report.aspx?c ompid=18050
Fascinating site ..tells you all about everywhere !