Brooke, son of a Dublin painter, worked predominantly as an illustrator, first working for The Satirist, where he was succeeded by George Cruikshank. He also illustrated books, and exhibited several times at the Royal Academy, London. It is possible that the present sketch was a study for an unrealised print.
Westminster Bridge was begun in 1811 and opened in 1817. Its opening was also depicted by John Constable (Tate Britain), amongst others.