Miles was born in Edgbaston in Birmingham, and learnt the game at an early age. In 1968 he won the British under-14 championship, and in 1973 won the silver medal at the World Junior Chess Championship at Teeside, his first important event against international competition. He won the title the following year in Manila.
Miles entered the University of Sheffield to study maths, but dropped out to concentrate on chess. In 1976, he became the first ever Grandmaster from the United Kingdom, narrowly beating Raymond Keene to the accolade (William Hartston came close to beating them both to it in the early 1970s). In so doing, he won a £5,000 prize.
Miles had a string of good results in the late 1970s and 1980s, and his success is considered to be one of the most important factors in the explosion in the number of strong British players around that time - shortly after Miles became a GM, Keene, John Nunn, Jon Speelman and a number of others followed him. Miles won games against a number of former World Chess Champions, including Vassily Smyslov, Mikhail Tal and Boris Spassky.
Most famously, in 1980 at the European Team Championship in Skara, he beat reigning world champion Anatoly Karpov with black using the extremely unusual opening 1. e4 a6!? (see algebraic notation), a line he had apparently learnt from weird-openings enthusiast, Michael Basman. Miles beat Karpov again three years later in Bath (this game was part of the BBC's Mastergame series, but was never shown on television due to a technicians strike).
Miles won the British Championship just once, in 1982 when the event was held in Torquay. One of his best results was his win at the Tilburg tournament in 1984. The following year, he tied for first there with Robert Hübner and Viktor Korchnoi, playing several of his games while lying face-down on a table, having injured his back.
Against Gary Kasparov, on the other hand, Miles had little success, not winning a game against him, and losing a 1986 match in Basel against him by the overwhelming score of 5.5 - 0.5. Following this encounter, Miles described Kasparov as a "monster with a thousand eyes who sees all" (some sources alternatively quote Miles as having the opinion that Kasparov had 22 or 27 eyes).
Miles was in many ways a controversial figure. Once, in the last round of a tournament, with both himself and his opponent needing a draw to tie for first, he agreed a draw without playing any moves. The arbiter decided to give both players no points for this non-game. This sparked a hefty amount of correspondence in British chess journals.
Miles also had his disagreements with chess authorities and with his fellow English players, particularly Keene. Miles made accusations regarding payments that Keene had received from the British Chess Federation for acting as his second (assistant) in the 1985 Interzonal tournament in Turin. Miles became rather obsessed with the affair, eventually suffering a mental breakdown over it. He was arrested in September 1987 in Downing Street, apparently under the belief that he had to speak to then-Prime Minister Margaret Thatcher about the matter. He was subsequently hospitalised for two months.
Shortly after this, he moved to the United States. He finished last in the 1988 US Championship, but continued to play there and had some good results. In 1991 he played in the Championship of Australia, but he eventually moved back to England, and began to represent his home country again.
Miles continued to play in the United States, however, tying for first in the 1999 Continental Open in Los Angeles with Alexander Beliavsky, Lubomir Ftacnik and Suat Atalik. Another good result later in his career was at the knock-out PCA Intel Rapid Chess Grand Prix in London in 1995, where he knocked out Vladimir Kramnik in the first round and Loek van Wely in the second (he was eventually knocked out in the semi-final by another English player, Michael Adams). He also won the Capablanca Memorial in Cuba four times.
Miles played in the 2001 British Championship, but withdrew before the final round, apparently because of ill-health. His final two games before his death were short draws in the Four Nations Chess League.
Miles was noted for his acerbic wit. His review of Eric Schiller's book Unorthodox Chess Openings (Cardoza Publishing, 1998) which appeared in Kingpin consisted of just two words: "Utter crap."
Miles suffered from diabetes, and a post mortem found that this contributed to his death by heart failure in 2001. His body was found at his home in Harborne, Birmingham after a friend called on him to take him to a bridge club. There was a minute's silence before the seventh round of the European Team Championships in León in Spain in his memory.