E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A Banbury-mani.e. a Puritan (Ben Jonson); a bigot. From the reign of Elizabeth to that of Charles II. Banbury was noted for its number of Puritans and its religious zeal.
As thin as Banbury cheese. In Jack Drums Entertainment we read, You are like a Banbury cheese, nothing but paring; and Bardolph compares Slender to Banbury cheese (Merry Wives, i. 1). The Banbury cheese is a rich milk cheese about an inch in thickness.