His family was from Edgbaston and he was born in Birmingham, England in 1759 and studied law at Lincoln's Inn in London. He was called to the bar in 1791. In 1798, he was appointed judge in the Court of King's Bench of Upper Canada. In 1800, he was elected to the 3rd Parliament of Upper Canada representing Durham, Simcoe and 1st York. However, a petition was raised citing irregularities on the part of his agent and he was unseated. Angus Macdonell won the seat in a by-election.
He presided over the trial of John Small for the murder of John White in a duel. Small was set free. In 1802, he became chief justice for Upper Canada succeeding John Elmsley and, in 1803, he was appointed to the Executive Council for the province.
In 1805, he became Chief Justice of Lower Canada and a member of the Executive Council of Lower Canada despite support for another candidate, Jonathan Sewell, by the upper class of the province and the lieutenant governor. He was named speaker for the Legislative Council of Lower Canada in January 1808.
He died of a fever at Quebec City in 1808, while in office.
- "Biography". Dictionnaire des parlementaires du Québec de 1792 à nos jours (in French). National Assembly of Quebec.
- "ALLCOCK, HENRY," by Frederick H. Armstrong, Dictionary of Canadian Biography, vol. 5, University of Toronto/Université Laval, 2003–
- "Henry Alcock" Find A Grave.
| Chief Justice of Upper Canada
| Chief Justice of Lower Canada