He was lord mayor of the city in 1674. In February 1692-1693 Brewster gave evidence before the Irish House of Commons on certain public abuses in Ireland, and in 1698 was appointed one of seven commissioners to inquire into the forfeited estates in Ireland.
The commissioners disagreed among themselves, and when the report was delivered in the following year it was signed by only four of the members of the commission. The other three, the Earl of Drogheda, Sir Richard Levinge, and Sir F. Brewster, having refused to sign it because they thought it false and ill-grounded in several particulars.
