Henry graduated from Oxford in 1652 and was ordained in 1657. He was the eldest son of John Henry, keeper of the orchard at Whitehall, and was born at Whitehall on 24 August 1631. His father, son of Henry Williams, was Welsh, born at Briton Ferry, Glamorganshire, on 10 July 1590, and took his father's name; he rose to be page of the backstairs to James, Duke of York, and was buried at St. Margaret's, Westminster, on 2 March 1652. His mother, Magdalen, daughter of Henry Rochdale, was baptised at St. Martin's-in-the-Fields on 19 October 1599, and died on 6 March 1645.
Philip Herbert, 4th Earl of Pembroke, in whose service his father had been, was his godfather. As a child he was playmate to the princes Charles and James, and kept to his dying day a book given him by the latter. Archbishop William Laud took notice of him for his readiness in opening the watergate when Laud came late from the council to cross to Lambeth. His father took him to see Laud in prison in the Tower of London, when the archbishop gave him some money. After preliminary schooling he was admitted in 1643 to Westminster School, and became a favourite pupil of Richard Busby. His mother, a Puritan, got leave for him to attend the early lecture at Westminster Abbey; but to Busby's diligence in preparing him for the communion he ascribes his adoption of a religious life in 1647.
In May 1647 Henry was elected to a studentship at Christ Church, Oxford, and went into residence on 15 December. He was admitted student on 24 March 1648, just before the parliamentary visitation, which removed Underwood, his tutor, substituting William Finmore (afterwards archdeacon of Chester). While at home on leave in January 1649 he saw Charles I, going on foot daily to his trial, who once spoke to his father. Of Charles's execution he gave an eye-witness account. He graduated B.A. in 1649 and M.A. on 10 December 1652. His father's death left the family in financial difficulties.
Henry preached his first sermon at South Hinksey, Oxfordshire, on 9 January 1653. On the introduction of Francis Palmer, afterwards professor of moral philosophy, he was engaged (30 September) by John Puleston, justice of the common pleas, as tutor to his sons at Emral, Flintshire, and preacher at Worthenbury Chapel, in the parish of Bangor-is-coed, same county. In 1654 he was with his pupils at Oxford; from 1655 he was constantly at Worthenbury. The rector of Bangor was Henry Bridgeman, but the living had been sequestered in 1646. Robert Fogg, the parliamentary incumbent, put in a caveat (14 Sept. 1657) against Henry's ordination as minister of Worthenbury, but afterwards withdrew it. Accordingly, having undergone an examination by the fourth Shropshire classis (constituted by parliament, April 1647), he was ordained with five others at Prees, Shropshire, on 16 September 1657. He made a strongly Calvinistic confession, but said nothing about church government. His ideal was a modified episcopacy on James Ussher's system.
In 1658 a commission of ecclesiastical promotions took Worthenbury Chapel out of Bangor parish, making it with Worthenbury Church (a donative) a new parish, of which Henry was incumbent. He declined the vicarage of Wrexham, Denbighshire, in March 1659, refusing shortly afterwards a living near London. He appears to have sympathised with the royalist rising under Sir George Booth in August 1659. Mrs. Puleston died in 1658, and the judge on 5 September 1659. Roger Puleston, their eldest son, had no love for his tutor; they had even come to blows (16 September 1656).
At the Restoration, which Henry, then newly married, welcomed, Bridgeman resumed the rectory of Bangor, and Henry's position was simply that of his curate at Worthenbury Chapel. In September 1660 he was presented at Flint assizes with Fogg and Richard Steel for not reading the common prayer, and again at the spring assizes, without effect. He had taken the oath of allegiance, but refusing reordination he was incapable of preferment. On 24 October 1661 Bridgeman, having failed to arrange matters, came to Worthenbury and read Henry's discharge before a crowd. Henry showed some feeling, but was allowed to preach farewell sermons on 27 October. The Uniformity Act of 1662, which took effect on 24 August 1662, silenced him. He surrendered his house and annuity for £100, to avoid litigation, and left Worthenbury for Broad Oak, Flintshire, a property settled upon his wife.
He consulted John Fell, then dean of Christ Church, about his difficulties. His main objection was re-ordination, which he reckoned simony. On 10 October 1663 he was apprehended with thirteen others and imprisoned for four days at Hanmer, Flintshire, on suspicion of an insurrectionary plot. On 15 March 1665 he was cited to Malpas, Cheshire, for baptising one of his own children; at the end of the month he was treated as a layman, and was made sub-collector of tax for the township of Iscoyd. The Five Mile Act of 1665 placed him in a difficulty, Broad Oak being four reputed miles from Worthenbury; on actual measurement it was found to be sixty yards over the five miles. However, he removed for a season to Whitchurch, Shropshire. All this time he was a regular attendant at parish churches, his habit being to stand throughout the service; he forbore communicating simply on the ground of the kneeling posture.
In February 1668 he preached by request in the parish church of Betley, Staffordshire, a circumstance of which accounts were reported in the House of Commons. Not till the short-lived indulgence of 1672 did he resume his public ministry in his licensed house, still avoiding encroachment on church hours. On the withdrawal of the indulgence, he continued to preach without molestation till 1681, when he was fined for keeping conventicles. In 1682 he had a public discussion with quakers at Llanfyllin, Montgomeryshire, and was drawn into a debate on ordination at Oswestry, Shropshire, with William Lloyd, at that time bishop of St. Asaph, and Henry Dodwell the elder.
At the time of Monmouth's rebellion he was confined in Chester Castle for three weeks (July 1685) under a general order from the lord-lieutenant. He joined in a cautiously worded address (September 1687) to James II. In May 1688 he was placed on the commission of the peace for Flintshire, but declined to qualify. At the revolution he had great hopes of ‘comprehension.’ The terms of the Toleration Act he accepted with some reservations. He ministered at Broad Oak in an outbuilding near his house.
His last years were spent in pastoral work. He died at Broad Oak of a sudden attack of colic and stone, on 24 June 1696, and was buried on 27 June in Whitchurch Church, where a marble tablet was erected to his memory, bearing a Latin inscription by John Tylston, M.D., his son-in-law. In 1712, when the church was rebuilt, his body was removed to the churchyard, and the monument to the porch.
In 1844 a tablet bearing an English version of the epitaph was placed in the north aisle of the church, the original monument being transferred to Whitewell Chapel, near Broad Oak. Funeral sermons were preached at Broad Oak by Francis Tallents of Shrewsbury, James Owen of Oswestry, and Matthew Henry.
He married, on 26 April 1660, at Whitewell Chapel, Katharine (25 March 1629-25 May 1707), only child of Daniel Matthews of Bronington, Flintshire, and had two sons, John (3 May 1661-12 April 1667), and Matthew, and four daughters, all of whom married. A genealogy of his descendants, to 1844, was published by one of them, Sarah Lawrence of Leamington. One of her great nieces was Susan Lawrence, the Labour politician.
His Diaries and Letters, published in 1882, gives a detailed account of the nonconformist life of his period. His son Matthew was a notable commentator on the Bible and also a Presbyterian minister.