BRP ran a Cooper-Borgward F2 car and BRM F1 car in 1959, the latter being demolished in a spectacular crash at the Avus street circuit. BRP was the first Formula One team to sell the entire identity of the team in return for sponsorship income, when they became Yeoman Credit Racing for the season. The Yeoman Credit deal was passed to Reg Parnell Racing at the end of the year, and for the and seasons BRP was renamed the UDT Laystall Racing, as part of a new, similar sponsorship deal.

For , the team reverted to its original name and became a true constructor; they had been running Lotus 24s and Cooper T51s for the previous few seasons, and had tried to acquire the more modern, monocoque Lotus 25 without success. This caused chief designer, Tony Robinson, to design his own monocoque car, patterned very closely after the Lotus 25, but with a thicker skin and running a BRM V8 rather than the typical Coventry Climax engine run in the Lotus 25. This car is commonly referred to as the BRP-BRM and was raced by Innes Ireland and Trevor Taylor.

As a constructor, BRP took part in 13 Grand Prix rounds, scoring a total of 11 championship points. After the team was forced to withdraw from F1; BRP were denied membership of the Formula 1 Constructors Association which effectively deprived them of start money, then a significant factor in a team's income. BRPs were built for the Indianapolis 500 but enjoyed little succes.

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