Cox was born of obscure parentage at Whaddon, Buckinghamshire, in 1499 or 1500.
He was educated at the Benedictine priory of St Leonard Snelshall near Whaddon, at Eton, and at King's College, Cambridge, where he graduated B.A. in 1524. At Wolsey's invitation he became a member of the Cardinal's new foundation at Oxford, was incorporated B.A. in 1525, and created M.A. in 1526. In 1530 he was engaged in persuading the more unruly members of the university to approve of the King's divorce.
A premature expression of Lutheran views is said to have caused his departure from Oxford and even his imprisonment, but the records are silent on these sufferings which do not harmonise with his appointment as Master of the Royal Foundation at Eton.
In 1533 he appears as author of an ode on the coronation of Anne Boleyn, in 1535 he graduated B.D. at Cambridge, proceeding D.D. in 1537, and in the same year subscribing the Institution of a Christian Man. In 1540 he was one of the fifteen divines to whom were referred crucial questions on the sacraments and the seat of authority in the Church; his answers (printed in Pocock's Burnet, iii. 443–496) indicate a mind tending away from Catholicism, but susceptible to "The King's Doctrine"; and, indeed, Cox was one of the divines by whom Henry said the "King's Book" had been drawn up when he wished to impress upon the Regent Arran that it was not exclusively his own doing. Moreover, he was present at the examination of Barnes, subscribed the divorce of Anne of Cleves, and in that year of reaction became Archdeacon and Prebendary of Ely and Canon of Westminster.
He was employed on other royal business in 1541, was nominated to the projected Bishopric of Southwell, and was made King's Chaplain in 1542. In 1543 he was employed to ferret out the "Prebendaries' Plot" against Cranmer, and became the Archbishop's chancellor. In December, he was appointed Dean of Oseney (afterwards Christ Church) Oxford, and in July was made Almoner to Prince Edward, in whose education he took an active part. He was present at Dr Crome's recantation in 1546, denounced it as insincere and insufficient, and severely handled him before the Privy Council.