He was born in East Tuddenham, Norfolk and died at Hodsock Priory, near Worksop, Nottinghamshire. Mellish was the elder son of the Review Edward Mellish, rector of East Tuddenham and later Dean of Hereford and his wife, who was Elizabeth Jane Leigh.
Eton College.
He was educated at Eton College and at Trinity College, Cambridge. While at Cambridge University, he appeared in two first-class cricket matches for the university side, both of them against the Cambridge Town Club. In one, he opened the batting, in the other he played as a tail-end batsman.
Mellish left Cambridge without taking a degree.
In 1833 he became an officer in the British Army: he is recorded as a second lieutenant in 1833 and as a captain in 1842, but he sold his commission in 1846 and left the full-time army. Thereafter he served with the local Nottinghamshire militia and at his death in 1864 he was recorded as "Lieutenant-Colonel of the Royal Sherwood Foresters".
