The youngest child of Alexander Mitchell-Innes (1811–1886) of Ayton, and Whitehall (near Chirnside), Berwickshire, by his second spouse Fanny Augusta (1821–1902), daughter of James Vine, in Puckaster, Isle of Wight, Alfred was born at 2 Forres Street, Edinburgh.

He married (her second marriage) in 1919, Eveline (d. 28 December 1946), daughter of Sir William Miller, 1st Baronet of Manderston, Berwickshire.

In 1934, Mitchell-Innes and his wife contributed 25 Egyptian and oriental antiquities he had acquired from Egypt to the British Museum.

In 1899, he was appointed Under-Secretary of State for Finance in Egypt, where he founded Al Ahly SC on 24 April 1907.

', received an approving review from John Maynard Keynes,[3] which led to the publication of the second, 'Credit theory of money'.