Irwin came through the junior ranks of British motorsport, racing in the 1965 British Saloon Car Championship with Don Moore in a Morris Mini Cooper S before moving into Formula Three. He raced for The Checkered Flag team, which also fielded him in the 1966 Argentine Temporada, an off-season series that attracted top European Formula Three talent to South America.
In early 1966, Irwin drove The Checkered Flag's scarlet Brabham BT16 through the International Formula Three Temporada in Argentina — a multi-round championship staged at Buenos Aires, Rosario, and Mar del Plata. Irwin was fast from the outset: at Buenos Aires he posted the second-quickest qualifying time, and in the final race he overtook the leaders mid-race to take victory more than half a minute clear of second-placed Charles Crichton-Stuart, with Nasif Estéfano third. He remained a championship contender throughout the series, consistently among the quickest of the British contingent alongside Jonathan Williams and Piers Courage.
Irwin made his Formula One World Championship debut at the 1966 British Grand Prix, driving a Brabham BT22 entered by Brabham Racing Organisation. He moved to Reg Parnell Racing for 1967, where he drove the Lotus 25, BRM P261, and BRM P83 across the season. His best championship result came at the 1967 French Grand Prix, where he placed fifth to score two points — his total for the season and his career.
Beyond the championship, Irwin participated in several non-championship Formula One events in 1967, including the Race of Champions and the BRDC International Trophy. He also contested the 1967 Tasman Series driving a BRM P261, finishing eighth overall with a fourth place at Sandown and a third at Longford.
Alongside Formula One, Irwin raced in the European Formula Two Championship in both 1967 and 1968 for Lola Cars. In 1967 he finished sixth in the championship. His most notable Formula Two result came at Zolder in 1968, where he won the race — one of his final competitive outings before the accident that ended his career.
During practice for the 1968 1000 Kilometres of the Nürburgring, Irwin was testing the Ford P68, an aluminium monocoque sports prototype known for its handling difficulties. At the Flugplatz — a high-speed crest on the Nordschleife that sent cars airborne — the P68 lost control after landing, flipping end over end. Irwin sustained severe head injuries. He eventually recovered, but never raced again in top-level competition.
Irwin made a rare public appearance at the Thruxton Circuit's 40th anniversary celebrations in April 2008, where he was photographed alongside 1960s rivals. A three-quarter page interview and photograph appeared in the June 2008 issue of Motor Sport magazine. He has since lived in rural Rutland, largely out of the public eye, though he was reported in 2006 to have reconnected with a former rival after a chance meeting in London and to sometimes still experience flashbacks to the Nürburgring crash.