I've long written about unitarianism and its impact on the political theology of the American Founding. It's important to distinguish between theological unitarianism and Unitarianism as an "official denomination." Theological unitarianism is old and became en vogue during the Enlightenment, leading to official Unitarianism presenting itself at that later time.
The opening of the Essex Street Chapel in England in 1774 marked the first of its kind: They called themselves Unitarian. The preacher was Theophilus Lindsey. In attendance that day were among others Ben Franklin and Joseph Priestley.
Various obstacles had been placed in the way of opening a Chapel with so odious a name. It was intimated that the State would interfere to prevent such sacrilege. The enemies of the Chapel tried to hinder the judges at Westminster from granting license to a house in which the Godhead of Jesus would be denied and the scheme of his Atonement be explained away. Vexatious delays were interposed, and the judges were urged to pause before they authorized a form of Dissent that denied the foundations of dogma as well as the rules of church discipline. When the Chapel was opened, it was really opened without a license, without any written warrant from the authorities of the State. Its preacher might have been arrested, and its doors summarily closed. This fact, nevertheless, did not hinder nearly two hundred persons from coming together in the Upper Room; and it is mentioned that there were about ten coaches at the door; “which I was glad of,” says John Lee, the friend of the modest and glad preacher, “because it gave a degree of respectableness to the congregation in the eyes of the people living thereabouts.” There was a nobleman in the congregation, Lord Despenser, Dr. Franklin was there; and the famous Dr. Priestley; and Dr. Chambers and Dr. Hinchley, and other clergymen of the Establishment.