After finishing his studies, he was ordained in the Church of England at Rochester, Kent and served as Assistant Curate in Dartord, Kent from 1942-45. He served as Army Chaplain from 1945-47, including service in Palestine. From 1947-55, he served at Foots Cray in charge of St. Andrew's Sidcup; St. Mary's Woolwich in charge of St. Anne's, and Horton Bank Top, Bradford Yorkshire.

Boston moved to Canada in 1955, where he served with the Anglican Church of Canada until 1960 when he joined and was received into the ministry of the United Church of Canada. In 1961 he went back to England to teach at St. Michael's School in Heacham. In 1962 he returned to the United Church of Canada where he served in pastoral positions in La Have and Lower Muaquodoboit in Nova Scotia, Plaster Rock and Loggieville in New Brunswick, and the Rideau Lakes in Ontario until he retired in 1982.

Henry Boston became concerned regarding drug laws when he discovered that police were going undercover to pretend they were dealers in illegal drugs in order to arrest school children and that technically someone could be imprisoned for life for sharing marijuana with a friend.
He submitted a motion to the Miramichi Presbytery that the General Council of the United Church of Canada be asked to conduct a review of laws prohibiting substances.

He was convener of a committee in the Kingston Presbytery to study the appropriateness, effectiveness, and social side effects of current drug legislation, in response to and as part of a nation-wide review in the United Church of Canada.

He was Founding President of the British Columbia Anti-Prohibition League in 1992, and was re-elected for another term in 1996.

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