Fox was born in Scunthorpe and began his career with Sheffield Wednesday, making his debut aged just 15 years 8 months, a club record in a 2–0 victory over Leyton Orient. Unfortunately for Fox he broke his toe that day and lost his place to another younger keeper, Chris Turner. Following the arrival of Jack Charlton as manager in October 1977, Fox found himself in the reserves, Charlton liked big keepers who could kick the ball long into the opponents half. After spending time out on loan at Barnsley and a summer in the NASL with Team Hawaii, Stoke City paid £15,000 to sign Fox.
After spending the 1978–79 season in the reserves, Fox took over from Roger Jones as number 1 in April 1980 as Stoke battled against relegation. He kept two clean sheets in the final two games which City won to stay up. Taking advice from the experienced Denis Smith Fox was ever present for Stoke in 1980–81 and 1983–84 as he won the player of the year award in 1980–81, 1981–82 and 1989–90. Throughout his 15 years at the Victoria Ground Fox had to fight off competition and almost quit football after he felt he had been branded a cheat after being sent-off for handling outside of his area against Luton Town in September 1982. He was out injured for most of the awful 1984–85 season which saw Stoke relegated with a record low points tally. He was given a Testimonial against Everton in 1989 and was appointed captain by Alan Ball in early 1990.
Following his release aged 36, he joined Exeter City, initially as player-coach, being made manager in 1995 after the departure of Terry Cooper. His time at the helm at Exeter was one of consistent mid-table mediocrity. The club was never in any serious relegation danger, however. He left St James Park in January 2000, replaced by his assistant Noel Blake.
His son, David, is also a professional footballer. Fox was taken to court in July 2015 by former Stoke youth-team player George Blackstock who alleged that in the 1980s Fox assaulted and humiliated him in 'dressing-room pranks'. Fox was cleared of the claims in October 2015.