It is possible that he was illegitimate and his mother was a PARKER and his father a Thomas BRUSHETT hence the use of two names. (or vice versa) A Thomas BRUSHETT was bapt in Stoke Damerel in 1788, son of Thomas & Elizabeth. An Elizabeth BRUSHETT married in Stoke Damerel in 1798 to a Thomas BUTTERSWORTH. It's not a Devonshire name as far as I know.
In 1841 a Mary BRUSHETT aged 70 was living with a George & Eliza BRUSHETT in St Mary, Lambeth - possible relations?