Norton was born in London and was educated at Cambridge, and early became a secretary to the Protector Somerset. In 1555 he was admitted a student at the Inner Temple, and married Margery Cranmer, the daughter of the archbishop.
In 1562 Norton, who had served in an earlier parliament as the representative of Gatton, became M.P. for Berwick, and entered with great activity into politics. In religion he was inspired by the sentiments of his father-in-law, and was in possession of Cranmer's manuscript code of ecclesiastical law; this he permitted John Foxe to publish in 1571. He went to Rome on legal business, in 1579, and from 1580 to 1583, he frequently visited the Channel Islands as a commissioner to inquire into the status of these possessions.
Norton's Calvinism grew with years, and towards the end of his career he became a rabid fanatic. Norton held several interrogation sessions in the Tower of London using torture instruments such as the rack. The rack stretched the body apart, until the joints were dislocated and then separated from the rest of the body. His punishment of the Catholics, as their official censor from 1581 onwards, led to his being nicknamed "Rackmaster-General" and "Rackmaster Norton."
At last his turbulent puritanism made him an object of fear even to the English bishops; he was deprived of his office and thrown into the Tower. Walsingham presently released him, but Norton's health was undermined, and in March 1584 he died in his house at Sharpenhoe, Bedfordshire.
From his eighteenth year Norton had begun to compose verse. We find him connected with Jasper Heywood; as a writer of "sonnets" he contributed to Tottel's Miscellany, and in 1560 he composed, in company with Sackville, the earliest English tragedy, Gorboduc, which was performed before Elizabeth I in the Inner Temple on 18 January 1562.
Gorboduc was revised into a superior form, as The Tragedy of Ferrex and Porrex, in 1570. Norton's early lyrics have in the main disappeared. The most interesting of his numerous anti-Catholic pamphlets are those on the rebellion of Northumberland and on the projected marriage of Mary, Queen of Scots, to the Duke of Norfolk. Norton also translated Calvin's Institutes (1561) and Alexander Nowell's Catechism (1570).
Gorboduc appears in various dramatic collections, and was separately edited by W.D. Cooper (Shakespeare Society, 1847), and by Miss Toulmin Smith in Volkmoller's Englische Sprache-und Literatur-denkmale (1883). The best account of Norton, and his place in literary history, is that of Sidney Lee in his Dictionary of National Biography.