The T81 was designed ahead of the 1966 season, which introduced new 3.0-litre engine regulations that transformed the technical landscape of Formula One. Cooper selected the Maserati Tipo 9 V12 engine, which had originally displaced 2.5 litres and was bored out to 3 litres for the new formula. The Maserati units were supplied by the Chipstead Group, the marque's UK distributor, which had taken control of Cooper in April 1965. The engine had previously been tested in the interim T80 development car.
In chassis design, the T81 represented an important milestone for Cooper as the team's first monocoque construction, though this approach had already been standard practice in Formula One since Lotus introduced it with the Lotus 25 four years earlier. The car otherwise followed conventional design of the period, with a rear engine, front radiator, and inboard front suspension. It debuted in the non-championship 1966 Syracuse Grand Prix, where Rob Walker entered a car for Jo Siffert and Guy Ligier entered his own example. For the 1967 season, strenuous efforts were made to reduce weight in a revised version designated the T81B.
The T81 made its World Championship debut at the 1966 Monaco Grand Prix with Jochen Rindt and Richie Ginther as the works drivers. Both retired with mechanical problems. The team ran up to three works entries at races alongside several privateer cars, leading to suggestions that Cooper were overstretching their resources and that car preparation was suffering as a result.
Despite the early struggles, John Surtees — who had replaced Ginther after walking out on Ferrari — delivered the T81's first victory in the final race of the 1966 season at the Mexican Grand Prix. His successor, Pedro Rodriguez, then won the very next championship round, the 1967 season opener in South Africa, giving the T81 back-to-back victories across consecutive seasons.
The T81B variant made its race debut with Rindt at the 1967 Monaco Grand Prix. Cooper finished third in the Constructors' Championship in both 1966 and 1967, their highest position since 1962.
The T81's last championship race came at the start of the 1968 season in South Africa, when privateers Jo Siffert and Jo Bonnier campaigned examples while the works team had already moved to the successor T86 chassis. Cooper folded at the end of 1968, meaning the T81 holds the distinction of being the last Cooper to win a World Championship Grand Prix.
Across its 21-race lifespan, the T81 and T81B combined for 85 entries, 2 wins, 1 pole position, 6 podiums, and 23 points finishes, accumulating 74 championship points. In the context of Cooper's history, the T81 represented the last moment of genuine competitiveness for a constructor that had dominated Formula One at the turn of the decade.