A Leicestershire county cricketer and England under-23 international, Graham joined Leicester City from Enderby Town, turning professional in November 1960 and becoming a key member of a memorable Foxes side.

He played two games short of 500 League appearances at Leicester and was loaned to Chesterfield in March 1976. Graham had a far greater impact at Saltergate than his bare statistics might suggest. Although here for just a dozen games and close to the twilight of his career, he was clearly still a remarkably good player: functional, rather than flamboyant, with a quiet authority and superb marshalling ability. As such, he had a visible influence on the development of Les Hunter. At the time that Cross joined Chesterfield were 19^th and falling, having conceded 58 goals in 34 games. On his March 13^th debut, the side kept their first clean sheet since Boxing Day and the side climbed out of relegation trouble.

The Spireites wanted to keep him after his loan period expired, but Brighton were able to offer a far higher wage and tempted him south.He helped them to promotion to Division Two in '76-7, then repeated the feat with Preston the following season, leaving Chesterfield fans with a distinctly lamentable feeling of what might have been.

After finishing the 1978-9 season with Lincoln City, Graham bowed out of the Football League and returned to Enderby Town, where it all began twenty years earlier.Graham managed Hinckley Athletic between 1981 and 1984, whereupon he became a director of the club.Around this time, he ran a post office in Hinckley.