Born in Hamilton, Lanarkshire, he attended St Cuthbert's Primary, Burnbank, before going on to St. Aloysius' College, Glasgow, and, later, Our Lady's High School, Motherwell.
He studied philosophy at Blairs College, Kincardineshire, from 1942 to 1944 and then served in the Royal Army Medical Corps, at home, in India and in Egypt.
After a year as assistant priest in St Bartholomew's, Coatbridge, he returned to Rome in 1952 where he took his doctorate in theology in 1954.
For more than ten years he represented Scotland on the Episcopal Board of the International Commission on English in the Liturgy (ICEL), and was its chairman from 1997 until 2002.
In 2013, it was revealed that Diocese priest Paul Moore had confessed to Taylor that he sexually abused a boy the year prior and that Taylor opted to send Moore to a treatment centre in Toronto and to Fort Augustus Abbey in the Highlands instead of turning him into the authorities.