Playing mostly as an inside forward or centre forward (and occasionally as a right-winger), Radford spent most of his career at Arsenal. He joined the club as an apprentice in 1962, turning professional in February 1964. He was a prolific goalscorer in the youth and reserve teams, before making his first-team debut against West Ham United on 21 March 1964 (his only appearance of the 1964-1965 season.
Radford was used slightly more the next season, playing 15 times, and became Arsenal"s youngest ever hat-trick scorer, against Wolves on 2 January 1965, at the age of 17 years and 315 days, a record that remains to this day.
By the start of 1965-1966 Radford was an Arsenal regular, and particularly blossomed under the stewardship of Bertie Mee. In 1968-1969, although he had been moved out to the right wing, he scored nineteen goals and reached the 1969 League Cup final.
By now, Radford had been moved up front again and continued to score regularly. He made his full England debut in a friendly against Romania on 15 January 1969.
He continued to play for Arsenal through the early 1970s, scoring another 19 goals in 1972-1973.
Unable to stake a place in the side, Radford moved on to West Ham United in December 1976 for £80,000. In all he played 481 times for Arsenal, scoring 149 goals, which makes him (as of 2011) Arsenal"s fourth all-time top scorer. After a year and 28 league appearances and no goals with the Hammers, Radford joined Blackburn Rovers in 1977.
He was moderately successful with the Second Division side, scoring ten times in 38 league appearances.
He left Rovers in 1978 and played for non-league Bishop"s Stortford before retiring. After retiring, he became a public landlord, and enjoyed several spells as manager of Bishop"s Stortford in the late 1980s and early 1990s.
He now also gives tours of Arsenal"s Emirates Stadium and appears as a football pundit on their television station: Arsenal television