Born at East Tuddenham, Norfolk, Mellish was the second son of the Very Rev. Edward Mellish, DD, Rector of the parish, who afterwards became Dean of Hereford, by his marriage to Elizabeth Jane Leigh, the daughter of the Rev. William Leigh, an earlier Dean of Hereford. His mother was a cousin of George Canning, who stood as godfather to Mellish.[1] His paternal grandfather was William Mellish, of Blyth Hall and Hodsock Priory, Nottinghamshire.[2]
On 4 August 1870, Mellish was appointed as Lord Justice of the Court of Appeal in Chancery.[5] The appointment was recommended by Prime Minister Gladstone, who had been Mellish's fag-master at Eton, although Gladstone had apparently forgotten the connection by the time of the appointment.[6] Mellish's appointment to the Chancery Court of Appeal was somewhat unusual, as he had practised almost entirely in the common law courts, not in equity.[7] On 12 August 1870, he was sworn of the Privy Council[8] and was afterwards knighted.[9] His appointment to the Privy Council entitled him to sit as a member of the Judicial Committee of the Privy Council, at that time the court of last resort for the British Empire beyond the seas.
Mellish was a lifelong sufferer from serious gout. One of the judges before whom he appeared later wrote "I have seen him arguing a difficult case before us while he was absolutely writhing with pain".[7] The illness compelled him on occasion to take absences from the bench.