He attended Corpus Christi College, Cambridge, receiving a Bachelor of Arts in 1621, and was made college librarian.
Early in 1643, Heath with much trouble obtained leave to go on the English mission and crossed from Dunkirk to Dover disguised as a sailor. A German gentleman paid for his passage and offered him further money for his journey, but, in the spirit of Saint Francis, Heath refused it and preferred to walk from Dover to London, begging his way. On the very night of his arrival, as Heath was resting on a door step, the master of the house gave him into custody as a shoplifter.
Some papers found in his cap betrayed his religion and he was taken to the Compter Prison.
The next day he was brought before the Lord Mayor, and, on confessing he was a priest, was sent to Newgate. Shortly afterwards he was examined by a Parliamentary committee, and again confessed his priesthood.
He was eventually indicted under the 1585 "Acting against Jesuits, Seminary priests and other such like disobedient persons" (27 Eliz c 2) for being a priest and present in the realm of Queen Elizabeth. While imprisoned at Tyburn he reconciled in the very cart one of the criminals that were executed with him.
He was allowed to hang until he was dead.
Henry Heath was among the eighty-five martyrs of England and Wales beatified by Pope John Paul II on 22 November 1987.