In a statement distributed by the UK's Press Association, his family said that Sir Bannister died peacefully, "surrounded by his family who were as loved by him as he was loved by them".
Bannister was recorded in Oxford on May 6, 1954 as the first to run under the four-minute mile, with 59.4 seconds mile. Bannister later wrote of the final moments of the race: "I felt at that moment that it was my chance to do one thing supremely well".
The man who came second in the race, Noah Ngeny of Kenya, also beat the previous world record - held by Algerian Noureddine Morceli since 1993 - with a time of 3:43.40.
Bannister's athletic achievement was made on May 6, 1954, in Oxford, England. It was the first time two men had run under 4 minutes in the same race.
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He was named the first chairman of the English Sports Council in 1971, and remained in that position until 1974. "Life has its physical challenges, but I take every day as it comes", he said.
He entered the 1952 Olympic Games in Helsinki as the United Kingdom record-holder in the mile, finishing a disappointing fourth in the 1,500-meter run.
Bannister and Landy then competed at the Empire Games, now called the Commonwealth Games, in Vancouver, British Columbia on August 9, 1954.
After retiring from competitive racing, Bannister spent two decades as a neurologist in private practice, then turned full-time to research, specializing in autonomic failure - illness characterized by the failure of the central nervous system to respond automatically to stimuli. Supposedly, the smartest and most plugged-in observers had concluded that human beings simply were not capable of running a mile in less than four minutes, and so Bannister's having done it was not only a historic achievement, but a scientific one too. "Those are real achievements". The current women's world record holder is Russian athlete Svetlana Masterkova with a time of 4 minutes, 12.56 seconds set on August 14, 1996 in Zurich.
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"There is not a single athlete of my generation who was not inspired by Roger and his achievements both on and off the track".
Lord Patten of Barnes, Chancellor of Oxford University, said: "My wife and I were very sad to hear about Roger Bannister's death".
"At the age of 88 he was still an active supporter of the University and we will miss him enormously". They had two sons and two daughters and lived only minutes away from the track where he set the record.
Bannister outlived his 4-minute mile pacemakers: Brasher, who founded the London Marathon, died in 2003 at the age of 74.
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