Agnew was the son of Sir Andrew Agnew, 8th Baronet and Lady Mary Arabella Louisa Noel, and succeeded his father as 9th Baronet, of Lochnaw on the latter's death on 25 March 1892.[1] On his own death in 1928 he was succeeded in the baronetcy by his nephew Fulque Agnew.
He married Gertrude Vernon, daughter of Hon. Gowran Charles Vernon and Caroline Fazakerley, on 15 October 1889,[6] but the marriage produced no children. Lady Agnew was the subject of a famous portrait by John Singer Sargent.