Henry was the second son of Sir Edward Norreys of Yattendon Castle, Berkshire, who took part in the Battle of Stoke in 1487, and was then knighted, by his wife Frideswide, daughter of Francis, Viscount Lovel. Henry came to Court in youth, was appointed Gentleman of the King's Chamber and was soon one of the most intimate friends of King Henry VIII. The King made him many grants and his influence at Court grew rapidly.

On 8th June 1515, Henry was made Keeper of the Park of Foliejon in Winkfield, Berkshire, an office which had been held by his father. On 17th February 1518, he became weigher at the common beam at Southampton, then the great mart of the Italian merchants. On 28th January 1519, he was appointed Bailiff of Ewelme in Oxfordshire. He was also Keeper of the King's Privy Purse. In 1519, he received an annuity of fifty marks (£33.6s 8d) and was at the Field of the Cloth of Gold in 1520, along with his Uncles, Richard Norreys and Sir Thomas Fettiplace. On 12th September 1523, he received the Keepership of Langley New Park in Buckinghamshire and was made Bailiff of Watlington. Henry early took the side against Wolsey and was one of the main instruments in bringing about his fall. Wolsey certainly recommended him for promotion in a letter of 5th July 1528; but it may be assumed from the letter itself that this was rather done to secure Henry's favour for the writer himself than with the idea that Norreys had any need of the Cardinal's influence.

Henry adhered closely to Anne Boleyn while she was gaining her position at Court and became one of her intimate friends and a leader of the faction that supported her proud pretensions to control the State. He had the sweating sickness in 1528 and, on 25th October 1629, gratified his enmity to Wolsey by being present when he resigned the Great Seal. On 24th October, Henry was the only attendant on the King, when he went, with Anne and her mother, to inspect Wolsey's property. Norreys was the bearer of the King's kind message to Wolsey, at Putney, about the same time, and seems to have been affected by Wolsey's fallen condition. In the same year, Henry received a grant of £100 a year from the revenues of the See of Winchester and was soon promoted to be Groom of the Stole. In 1531, he was made Chamberlain of North Wales; in November 1532, he was again ill; in 1534, he was appointed Constable of Beaumaris Castle (Anglesey); in 1535, he received various manors which Sir Thomas More had held. He was present at the execution of the Charterhouse monks, on 4th May 1535, and Henry granted him the important Constableship of Wallingford  Castle (29th November 1535); and he was generally regarded as the King's agent in the promotion of the new marriage with Lady Jane Seymour.

In April 1536, Queen Anne had some talk with Sir Francis Weston, who hinted to her that Norreys loved her. She, afterwards, spoke to Norreys about it and, jokingly, said that he was waiting for dead men's shoes. He protested and, in the end, she asked him to contradict any rumours he might hear about her conduct. But Norreys had many enemies and his alleged intimacy with Anne was carefully reported to Thomas Cromwell. On 1st May 1536, Norreys took part in a tournament at Greenwich and, at the close, Henry spoke to Norreys, telling him that he was suspected of an intrigue with Anne and urging him to confess. He was then arrested and taken to the Tower by Sir William FitzWilliam. He was tried on 12th May in Westminster Hall. He pleaded not guilty, but was found guilty and executed on 17th May. He was buried in the churchyard of the Tower of London.

There is little reason to think that he had behaved in any way improperly with the Queen. Most of the jury seem to have been officials or open to suspicion of partiality. Apparently, Queen Elizabeth always honoured his memory, believing that he died ‘in a noble cause and in the justification of her mother's innocence.’ At the time of his arrest, he was contemplating a second marriage with Margaret Shelton and, both his interest and his long experience as a courtier, would doubtless have deterred him from encountering the danger certain to spring from a liaison with Anne Boleyn. His knowledge of the King would also have taught him that his ruin and death must be the consequence of such desperate adventures.

Henry married Mary, daughter of Thomas Fiennes, Lord Dacre of the South. She died before 1530 and, by her, he had a son Henry, 1st Baron Norreys of Rycote. Another son, Edward, born in 1524, but died on 16th July 1529. A daughter Mary married, firstly, Sir George Carew, and, secondly, Sir Arthur Champernowne.

Heavily Edited from Sidney Lee's 'Dictionary of National Biography' (1895)