Background
Parker was the eldest son of John Parker (1703–1768) of Boringdon Hall, Plympton, and Saltram House, by his wife Catherine Poulett (1706–1758), whom he married in 1725, daughter of John Poulett, 1st Earl Poulett. He had a sister Henrietta Parker (d1808) and a younger brother, Montagu Edmund Parker (1737–1813) of Whiteway House, near Chudleigh (purchased by his grandfather George Parker (d1743) who also purchased Saltram), Sheriff of Devon in 1789, who married in 1775 Charity Ourry (1752–1786), daughter of Admiral Paul Ourry, by whom he had issue Montague E. Parker (1778–1831) whose daughter Harriet Parker (1809–1897) married in 1842, as her second husband, her second cousin Edmund Parker, 2nd Earl of Morley (1810–1864).