Premise: Tothill Fields Bridewell (also known as Tothill Fields Prison and Westminster Bridewell) was a prison located in the Westminster area of central London between 1618 and 1884. It was named 'Bridewell' after the Bridewell Palace, which during the 16th century had become one of the City of London's most important prisons. Tothill Fields later became the Westminster House of Correction.
Hypothesis: It was named 'Bridewell' after the small Bridewell Palace.