Inchcape was the son of Kenneth Mackay, 2nd Earl of Inchcape, and his first wife Joan Moriarty, daughter of John Francis Moriarty, Lord Justice of the Irish Court of Appeal.
His half-brother on his father's side was the life peer Simon Mackay, Baron Tanlaw.
Between 12 February 1941 and their divorce in 1954, Lord Inchcape was married to Aline Thorn Pease, widow of an R.A.F.
officer,[1] and daughter of Sir Richard Pease, 2nd Baronet and Jeanette Thorn Kissel.
They had four children – On 3 February 1965 he married Caroline Harrison, daughter of Cholmeley Dering Cholmeley-Harrison and Barbara Mary Corisande Bellew, with whom he had three sons (two by birth and one by adoption) In 1969, The Countess of Inchcape became Lloyd's of London's first female Name.