The P57 model was designed by Tony Rudd for the 1961 Championship. According to the new regulations, the engines had a displacement limited to 1,500cc, and the consequent reduction in available power forced the manufacturers to renew their models.

The quickest to react was Ferrari, which won the Drivers 'and Constructors' Championships that year. While at Lotus, Colin Chapman was preparing his first revolution in F1, with the model 25, at BRM, Tony Rudd designed a conventional multitubular spaceframe chassis, which would be equipped with a brand new V8 engine. The P57 chassis had suspensions with double wishbones and outboard springs over dampers, the brakes were disc and the tires supplied by Dunlop.

A delay in engine availability led BRM to use the customer 4-cilinder Coventry-Climax during the 1961 season. As the set proved to be very heavy in the face of competition, the year ended with poor results.

For the following year Tony Rudd had the new engines available, which delivered about 190hp at 11,000rpm. Using a 5-speed gearbox from the brand and a ZF transmission, BRM outperformed Ferrari and, taking advantage of the low reliability of the new Lotus 25, won the Drivers 'Championship, the first for Briton Graham Hill, and the Constructors' Championship, which would become the only one, for the British brand.

As the brand's first driver, Graham Hill won 4 races and his American teammate Richie Ginther got enough points to secure the Constructors title for BRM.

The P57 remained competitive the following season, with the same pair of drivers, achieving Hill two more victories and finishing in 2nd place in a Championship dominated by Jim Clark at the wheel of the revolutionary Lotus 25. Ritchie Ginther finished in 3rd place, guaranteeing for BRM the Constructors' runner-up.

The P57 would remain in competition until 1965, registered by private teams.