He joined Fulham professionally in 1956 and remained a dependable performer for 13 years thereafter, though his chances at international level seemed to be restricted to a handful of caps at under-23 level, mainly due to the presence of Blackpool's Jimmy Armfield, who was the regular incumbent at No. 2 and played in the 1962 World Cup in Chile.
In April 1964, however, Armfield won his 41st cap in an embarrassing defeat against Scotland at Hampden Park. England coach Alf Ramsey duly tried out Cohen for his international debut a month later in a 2–1 win over Uruguay. With Armfield suffering an injury – timed appallingly with the World Cup imminent – Cohen went on to play in 21 of the next 23 internationals. Armfield managed two more caps in preparation for the 1966 tournament after regaining his fitness, but Cohen was Ramsey's first choice by the time the competition, which England was hosting, got underway.
Cohen was an immaculate performer in Ramsey's revolutionary team which played without conventional wide men, allowing extra strength in midfield and relying on young, stamina-based players like Martin Peters and Alan Ball to drift from centre to flank and back again as required. When these players were occupied in more central positions, or chasing high up the flank and needing support, attacking full backs like Cohen proved their extra worth.
As England got through a tough group containing Uruguay, Mexico and France, Cohen's unfussy performances were rightly seen as just as vital as the attention-grabbing displays from the likes of Bobby Charlton. Cohen maintained his form as England got past a thuggish Argentina in the last eight, and was unwittingly featured in one of the more memorable photographs of the tournament in the immediate aftermath of the game – Ramsey, livid at the Argentinians' violent approach (he later memorably called them "animals" in a post-match interview), ran to Cohen in order to prevent him swapping shirts with one of his opponents.
Three days later, one of Cohen's overlapping runs and clever near-post passes contributed to Charlton's clincher as the hosts edged past the splendid, if rather enigmatic, Portugal in the semi finals.
In the final against West Germany, Cohen won his 30th cap as vice-captain and was his usual immaculate self, though in a game full of incident and iconic individual contributions, his only notable moment of the match was managing to block the vicious last minute free kick from Lothar Emmerich which subsequently found its way across the England six-yard box for Wolfgang Weber to stroke home the late equaliser which forced extra-time. England ultimately won 4–2.
Cohen played seven of the next eight internationals before Ramsey decided to utilise some younger full backs in England's campaign for the 1968 European Championships. Cohen's 37th and final England appearance came in a 2–0 win over Northern Ireland at Wembley on 22 November 1967. He did not score for his country, though this was not unexpected for a man in his position. He was the first of England's 1966 XI to cease playing for his country.
Cohen served Fulham until March 1969, not winning any major trophies, before retiring from playing at the age of 29 due to injury.
Fulham had been relegated to the Second Division the season before he retired as a player and did not return to the top flight for 33 years. He ended his career with 459 appearances for the club, a figure surpassed by only five other players in Fulham's history. It would have been more but for the injury which forced his retirement before his 30th birthday. As a full back he also managed to score six League goals for Fulham. Cohen coached the Fulham youth team and the England under-23 team for a time, and also managed non-league Tonbridge.
Manchester United's legendary winger George Best described Cohen as "the best full back I ever played against". Alf Ramsey called Cohen "England's greatest right back". Cohen also bears the distinction of being the only Fulham player to have won a World Cup winner's medal while at the Cottagers.
Cohen was awarded the MBE in 2000, along with four team-mates from 1966 after a campaign from sections of the media who were surprised that the quintet had never been officially recognised for their part in England's success. The others were Ball, Wilson, Nobby Stiles and Roger Hunt.
In October 2016, a statue of Cohen was unveiled at Craven Cottage by club chairman Shahid Khan to commemorate their former player and mark the 50th anniversary of the England World Cup win. Cohen attended the ceremony. Hammersmith & Fulham Council announced that it was making the former footballer a freeman of the borough.
In a documentary on Channel 4 to find the greatest England XI, Cohen was given the right back spot by the public, ahead of Phil Neal and Gary Neville. He was one of four veterans of the 1966 team to make it.
Cohen published his autobiography in 2003, titled George Cohen: My Autobiography. (ISBN 9780755313976). Now retired, he is frequently a guest at functions around the country as well as at Craven Cottage raising money for cancer charities. He hosts a luncheon before every home game at Craven Cottage in the George Cohen Restaurant.
In 2010, Cohen criticized changes to the design of footballs following the intense criticism of the Adidas Jabulani used at the 2010 World Cup. Cohen was quoted: "Designers have constantly tried to create more goals by using lighter and lighter balls. It was thought they would fly further and everyone loves to see a 30-yard screamer bend into the top corner. But things have gone too far."
Despite his surname, Cohen is not Jewish, and neither were either of his parents. The surname was inherited from a Jewish great-grandfather. George was raised in the Church of England. He has been married to his wife Daphne since 1962; they have two sons. George's nephew Ben Cohen was an English rugby player and Rugby World Cup winner with England in 2003.
George Cohen ... was lauded by the Jewish, national and international press. ... [H]e rang up the editor to explain that he was not actually 'of the faith'. 'I have a Jewish great-grandfather,' he said, 'but that's it, really. Neither my father nor my mother was a Jew. I have always been Church of England.