He does have a sister Mary - Mary Elizabeth Brooks baptised 24 May 1795 - but I haven't found a marriage for her; he also had a sister Eliza Judith baptised 2 April 1797, Jane Sarah baptised 3 June 1804, and Anna Maria baptised 3 April 1806 - all at St James, Westminster.

Edited - I have discovered nothing else about any of the sisters.