Edmonds was born in Lusaka. His father was a British businessman and his mother was from Belgium. While living in Lusaka, Edmonds was educated at Gilbert Rennie High School. In his biography, Edmonds recounted that the school had magnificent academic and sporting facilities. He moved to England in 1966 and completed his secondary education at Cranbrook School in Kent before enrolling at Fitzwilliam College, Cambridge as a student of land economy.

Edmonds made his first-class debut for Cambridge University against Warwickshire on 24 April 1971. He opened the batting, making 10 and 3, and bowled without success as Warwickshire won by 109 runs. However, Edmonds would not have to wait long for success. In the following match against Leicestershire, he would record his first 5-wicket haul in an innings, taking 5/50, and back up with 4/48 in the second innings to help Cambridge University to a seven-wicket win. After taking 7/56 in the first innings of the annual University Match against Oxford University, finishing the match with his first 10-wicket haul in a first-class match, Edmonds made his debut for Middlesex in a thrilling match against Essex at Lord's Cricket Ground on 4 August. He bowled solidly, returning figures of 2/51 and 3/42, and was the last batsman in with Middlesex still needing 16 runs off the final two overs to win. In the end, Middlesex ran out of time and had to defend the final ball to escape with a draw, which they managed.

Edmonds made his debut for England in the Third Test of the 1975 Ashes series at Headingley. Defending a first innings of 288, England managed to dismiss Australia for 135, with Edmonds taking a stunning 5/28 on debut. His first Test wicket was Greg Chappell, caught by Derek Underwood, and then he trapped Ross Edwards in front next ball to be on a hat-trick.^[12] The match however had to be abandoned after vandals ruined the pitch, and the result was declared a draw.

At county level, Edmonds' Middlesex career coincided with that of John Emburey. The left- and right-arm spin combination was a powerful contribution towards Middlesex's success in the 1980s. They also combined at England level, although the pair often competed for the same place in the Test team.

After playing for Eastern Province in the Currie Cup competition during the 1975-76 season, Edmonds returned to England and straight into the English county season. Although Edmonds was more renown for his exploits with the ball, he could also deliver on occasion with the bat when needed. One such instance that illustrated this was the county match against Northamptonshire early in Middlesex's championship-winning 1976 season. In the second innings of that match, Middlesex appeared on the verge of losing by an innings when Edmonds came to the crease. He proceeded to bat aggressively but also sensibly, supported by Mike Gatting and Fred Titmus. By the time he was dismissed on 93, to that time his highest first-class score