Allam entered the British Saloon Car Championship for the first time in 1978 driving a Ford Capri 3.0, finishing second in class. He repeated that result in 1979 before stepping up to the TWR Rover Vitesse programme in 1981, taking Rover's first overall win in the championship that year. In 1982 he drove again for TWR Rover, winning the class title while paired for much of the season with Frank Sytner.
The 1983 season brought Allam together with teammates Steve Soper and Pete Lovett in the Rover outfit. The three drivers dominated the championship, easily securing the manufacturers title for Rover while Soper took the drivers crown. The success was erased from the record books, however, after the TWR Rovers were found in breach of regulations regarding engine installation, costing the team its results and handing the drivers championship to Andy Rouse.
Allam's talent translated well beyond British borders. At the 1984 Bathurst 1000 in Australia, driving a TWR Rover partnered by German co-driver Armin Hahne, he won the new Group A class — a significant international result for the TWR programme. Two years later, at the 1986 ETCC Tourist Trophy at Silverstone, Allam and co-driver Denny Hulme — former Formula One World Champion — won the prestigious event in a TWR-prepared Rover.
He was a regular competitor at the Bathurst 1000 through the late 1980s and into 1990. In 1985 he co-drove a TWR Jaguar XJS but retired early after engine damage caused by broken headlight glass. In 1988 he returned with Tom Walkinshaw in a fuel-injected Holden VL Commodore SS Group A SV, but suspension failure ended the race on lap five. Switching to Ford for the 1989 and 1990 events with Dick Johnson Racing, Allam achieved his best Bathurst result in 1990, partnering Paul Radisich to second place overall in a Sierra RS500.
Allam also contested the TVR Tuscan Challenge in the United Kingdom, taking the championship title in 1989.
Allam returned to the British Touring Car Championship (by then renamed from BSCC) in 1990 for Vic Lee Motorsport, driving a BMW M3 in the 2.0-litre class and finishing sixth in the series. In 1991 he joined the works Vauxhall team in a Cavalier, again placing sixth. He remained with Vauxhall for three further seasons, partnering John Cleland: 1992 brought two race wins and fourth place in the standings, while 1993 and 1994 saw ninth- and tenth-place finishes respectively.
Allam was replaced at Vauxhall by James Thompson for 1995, though he made a one-off comeback the same year at Knockhill to substitute for the injured Thompson.
In 2004 Allam was invited to compete in the BTCC Masters event at Donington Park, an invitational race organised by TOCA director Alan Gow for former champions and notable alumni of the series. Driving a SEAT Leon Cupra, he finished eighth in a field of sixteen.
From the mid-1990s onward Allam served as Driving Standards Advisor to the BTCC, assisting the Clerk of the Course in adjudicating on-track incidents. He was formally reappointed to that role in May 2011. Away from motorsport, he has worked as Head of Business for Allam Motor Services in Epsom, a dealership covering Skoda sales and Vauxhall servicing.
Allam's career spanned the late-1970s amateur era through to the professional Super Touring era of the 1990s, and he remained competitive throughout. His partnership with TWR yielded international victories at Bathurst and Silverstone, and his class win at the 1984 Bathurst 1000 formed part of the broader TWR touring car success story that dominated the decade. Though the 1983 BSCC results were expunged, his role alongside Soper and Lovett in that dominant Rover campaign is recognised as one of the most complete team performances the championship had seen. His later administrative contributions to the BTCC extended his connection to British touring car racing well into the twenty-first century.