I would have to check on the Mayor bit, but I can confirm that Jane B Du Boulay was elected to the Parish Council in Sandwich on 7th May 1987. (http://www.dover.gov.uk/pdf/PARISH87.PDF)
She did not stand for re-election in 1991.
Unfortunately, the site does not have any record of precious elections. I will try to find a list of mayors - probably when I next go to Sandwich.