He was born at Ardquin, County Down, the second son of Robert Echlin and great-grandson of Robert Echlin, who was Bishop of Down and Connor from 1612 to 1635. His mother was Mary Leslie, daughter of Henry Leslie, Bishop of Meath (died 1661) and his wife Jane Swinton. His father died when his children were still very young, and seems to have left his family in some financial difficulty. Henry's younger brother was Lieutenant-General Robert Echlin (c.1657-c.1723), commander of the 6th (Inniskilling) Dragoons, and later a prominent Jacobite.
He gained useful experience by working in the courts as a clerk while still in his teens, no doubt to supplement his income, and at the same time attended the University of Dublin; he matriculated in 1667, was Scholar in 1668, and became Master of Arts in 1703. He practiced for some time as an attorney, then entered Lincoln's Inn in 1672 and the King's Inns in 1677.
In 1683, he was appointed Third Serjeant-at-law. Since he was barely thirty and had only been in practice at the Irish Bar for six years, his appointment caused some surprise. Like almost all legal appointments at the time, it was largely due to the influence of James Butler, 1st Duke of Ormonde, the Lord Lieutenant of Ireland; Echlin also had the support of Sir John Temple, the Solicitor General for Ireland, who justified the appointment as follows:
"He hath been seven or eight years at the Bar, and very studious and industrious in his profession, though I cannot say that either he or Mr Sprigg are yet in any great practice."
He was dismissed as Serjeant in 1687, presumably as part of the campaign by King James II to appoint as many Roman Catholics as possible to senior legal offices.
At the Glorious Revolution, he took his family to England to be out of harm's way, but he returned to Ireland in 1690 and was made second Baron of the Court of Exchequer (Ireland); he later transferred to the Court of King's Bench (Ireland), then returned to the Exchequer. He regularly attended on the Irish House of Lords; he was knighted in 1692 and sat on a commission to assess the estates of those Jacobites who had fled to France. He was required to explain to the Lords why he had asked a bishop who had asked to give unsworn evidence in court to swear an oath (rather ironic given the number of bishops in his own family tree). He lobbied in 1706 to become Chief Baron of the Irish Exchequer, but was passed over, supposedly on the grounds of ill health, although he was well enough to go regularly on assize in Ulster.
In 1713-4, political life was greatly complicated by a feud between the central Government and Dublin Corporation. Echlin, along with his colleagues, signed a number of reports on the matter, which were considered to give a partisan view of the affair. Questioned years later by the Irish House of Commons on his actions, he admitted frankly that he knew little about the affair, but had signed whatever reports were placed before him for fear of losing his office if he refused.
In 1714, on the death of Queen Anne, her Irish judges were removed en blocand were in temporary disgrace; (one, Anthony Upton, later committed suicide), but Echlin's reputation did not suffer permanently. Ball says that his loyalty to the House of Hanover was never seriously in question, although suspicions about his loyalty would have been natural enough from 1715 onwards, when his brother, General Robert Echlin, embittered by what he saw as the Crown's failure to reward him properly for his long military service, fled to France and became a prominent Jacobite. The brothers do not seem to have been personally close, and there is no evidence that Henry, despite his increasing wealth, ever helped his brother financially.
In 1721, Henry was made a baronet. He died in 1725.
He married Agnes, daughter of the Reverend William Mussen, and they had three sons and a daughter. Robert, the eldest son, died in 1706. He had married Penelope Eustace, daughter and co-heiress of Sir Maurice Eustace of Harristown, County Kildare, and the title passed to their son, Sir Robert Echlin, 2nd Baronet.
The main Echlin estate was Kenure House at Rush, County Dublin, which had once belonged to the Duke of Ormonde: only traces of Kenure now remain. Echlin also owned Clonagh Castle in Kildare and a town house at Winetavern Street, Dublin.
There is a sympathetic account of his character, which notes in particular his abiding passion for books, from the author and bookseller John Dunton, who met him in 1698:
"Baron Echlin is a person of great honour, and of a greatness of soul beyond most that I ever heard of. He is such a universal lover of books that very few if any shall escape him whatever their cost. He has a very large and curious library, yet is as inquisitive still after rarities as if he had none."