Dearing was born in Kingston upon Hull. He was the eldest son of a docks clerk. His father was killed whilst fire watching during an air raid.
Dearing attended Willerby Carr Lane County Primary School before going on to Malet Lambert Grammar School. At the University of Hull, he gained a BSc in Economics in 1954 during a two-year break from the Ministry of Power.
Dearing joined the civil service as a 16-year-old clerical officer in 1946. By 1967, aged 37, he was one of the two deputy heads of the coal division of the Ministry of Power, with the rank of assistant secretary.
In 1967 Dearing had responsibility for two major issues arising from the 1966 Aberfan disaster, in which a huge coal waste tip collapsed onto the town of Aberfan in Wales, killing 144 people including 116 school children. Dearing briefed the then Minister, Richard Marsh on the question of the possible removal of Lord Robens as chair of the National Coal Board in the wake of the damning Davies Report, which found the Coal Board wholly responsible for the disaster, and on the issue of the removal of the remaining tips above the town.
He was later the fifth Chancellor of the University of Nottingham (1993-2000) and the author of the Dearing Report into Higher Education. The annual teaching awards at Nottingham (initiated in 1999) are named after Lord Dearing, as is a more recent series of teaching fellowships. The main education building on the Jubilee Campus is also named after him. The name Dearing Report is also applied to the 2001 report which he chaired: "The Way Ahead: Church of England schools in the new millennium".
He married Margaret (Meg) Patricia Riley in 1954, whom he had met in a Methodist church when living in Bermondsey. They had two daughters and lived in Surbiton. Dearing had had cancer since the mid-1990s.
In the 1979 New Year Honours, Dearing was appointed to the Order of the Bath as a Companion (CB) and in the 1984 Birthday Honours, Dearing was knighted and the Queen conferred the honour upon him on 21 August 1984.
In 2000, Lord Dearing visited Malet Lambert School Language College, Kingston upon Hull, to open a new building constructed for the use of science and geography, it being named the Dearing Centre. Similarly, in 2004, he visited Hymers College, Kingston upon Hull, whereupon he opened the new science block with the purpose of educating the children in the areas of physics and chemistry. The Dearing Building on the University of Nottingham's Jubilee Campus is named after this former chancellor of the university.