The son of a Lincolnshire solicitor, Mossop became a member of the Chelsea Vestry, and was nominated by them to be a member of the Metropolitan Board of Works in 1885. He remained a member of the board until its abolition in 1889. He unsuccessfully sought election to the London County Council, the successor body to the Metropolitan Board, in January 1889.
He died at his home in Putney in 1901, aged 67.
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