Sir John Radcliffe's father, Robert Radcliffe, 1st Earl of Sussex, married firstly, shortly after 23 July 1505, Elizabeth Stafford, the elder daughter of Henry Stafford, 2nd Duke of Buckingham, and Katherine Woodville, by whom he had three sons:[2] After Elizabeth Stafford's death, Sussex married secondly, by 1 September 1532, Margaret Stanley, the only daughter[5] of Thomas Stanley, 2nd Earl of Derby, and Anne Hastings, the daughter of Edward Hastings, 2nd Baron Hastings, by whom he had two daughters, Jane, who married Anthony Browne, 1st Viscount Montague, and Anne, who married Thomas Wharton, 2nd Baron Wharton.
Sussex died on 27 November 1542, and his widow, Sir John Radcliffe's mother, Mary, married, on 19 December 1545, as his second wife, Henry FitzAlan, Earl of Arundel (d. 24 February 1580).
However, by his mother's second marriage Sir John Radcliffe was a stepbrother of the Earl of Arundel's three children by his first marriage to Katherine Grey (b. in or after 1509, d. 1542), second daughter of Thomas Grey, 2nd Marquess of Dorset (1477–1530), and his second wife, Margaret Wotton.
His stepsister, Mary Fitzalan, translated into Latin 'four collections of sententiae, from Greek and English sources' (now BL, Royal MSS 12 A.i–iv), which she dedicated as New Year's gifts to her father.
[10] Radcliffe's mother, Mary, died on 20 or 21 October 1557 at the Earl of Arundel's London house, Bath Place.