His parents were George Monckton-Arundell and Vere Gosling.
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They had four children: Mary Victoria Monckton (b. 1924), Celia Ella Vere Monckton (1925–1997), Isabel Cynthia Monckton (b. 1926) and Simon George Robert Monckton-Arundell (1929–1971).
The fourth creation came in the Peerage of Ireland in 1727 when John Monckton was made Baron Killard, of the County of Clare, and Viscount Galway.
County Galway | Galway | Horatio Nelson, 1st Viscount Nelson | Viscount | Vickers Viscount | Bernard Montgomery, 1st Viscount Montgomery of Alamein | William Howe, 5th Viscount Howe | viscount | James Galway | Garnet Wolseley, 1st Viscount Wolseley | Charles Lyttelton, 10th Viscount Cobham | William Slim, 1st Viscount Slim | National University of Ireland, Galway | Edmund Allenby, 1st Viscount Allenby | William Lamb, 2nd Viscount Melbourne | Martin Galway | Julian Byng, 1st Viscount Byng of Vimy | Alan Brooke, 1st Viscount Alanbrooke | William Waldorf Astor, 1st Viscount Astor | James Bryce, 1st Viscount Bryce | Henry St John, 1st Viscount Bolingbroke | Henry John Temple, 3rd Viscount Palmerston | Edward Grey, 1st Viscount Grey of Fallodon | Charles Bathurst, 1st Viscount Bledisloe | Walter Runciman, 1st Viscount Runciman of Doxford | Viscount Falkland | Samuel Hood, 1st Viscount Hood | John Anderson, 1st Viscount Waverley | James Craig, 1st Viscount Craigavon | William Beresford, 1st Viscount Beresford |