His father died in 1943 of wounds received action in during World War II.
Cunliffe-Lister succeeded as the 2nd Earl of Swinton on the death of his grandfather in 1972 and served as Deputy Chief Whip in the House of Lords under Margaret Thatcher from 1982 to 1986.
In 1959, he married Susan Lilian Primrose Sinclair who was created a life peer as Baroness Masham of Ilton in 1970.
He was also formerly a member of the Countryside Commission and a director of the Leeds Permanent Building Society.
Dogged by illness for the last 10 years of his life, Swinton suffered a stroke and was disabled by its effects and those of Parkinson's disease.