Adrian Newey conceived the CG891 as a refined evolution of the aerodynamic philosophy he had introduced on the March 881. The carbon fibre monocoque was notably slimline, and an inboard gear cluster was adopted to allow a full-width diffuser panel at the rear of the chassis. Suspension used a push-rod double wishbone arrangement at both ends. The wheelbase measured 2,933 mm with a front track of 1,778 mm and a rear track of 1,651 mm.
Power came from a Judd EV 3.5-litre V8 engine in an exclusive arrangement with John Judd's Engine Developments company, rated at approximately 625 bhp with a maximum of 11,500 rpm. Because the Judd EV used a narrower vee angle of 78 degrees, a Magneti Marelli electronic ignition system replaced a conventional distributor. The car ran on Goodyear tyres with BP fuel and oil.
The designation "CG" honoured Cesare Gariboldi, a Leyton House March team manager who was killed in a road accident during the winter of 1988–1989. A total of five CG891 chassis were constructed over the course of the season. Sponsors on the sidepods and bodywork included Leyton House, BP, Philips, Autoglass, and Fiamm among others.
The CG891 did not appear at the opening rounds of the 1989 season; the March 881 continued to serve the team for the first two races while development was completed. The CG891 made its debut at the Monaco Grand Prix, where Gugelmin qualified fourteenth and Capelli twenty-second. Capelli experienced electrical problems during qualifying and had to revert to the 881 for part of the session. Both drivers retired from the Monaco race, though Capelli was still classified eleventh.
The French Grand Prix proved the most promising outing of the season. Capelli ran as high as second place before engine failure ended his race. Gugelmin, having taken over the spare car after a start-line accident destroyed his own CG891, went on to set the fastest lap of the race — the car's single fastest-lap distinction of the year — although he was classified as unfinished, nine laps behind the winner.
Gugelmin's best race results with the CG891 were three seventh-place finishes, in Belgium, Japan, and Australia. Capelli's only classified finishes were eleventh in Monaco and twelfth in Belgium. Reliability was hampered early in the season by the inboard gear cluster casing, which exhibited flex and caused gearbox failures; reinforcing the casing walls addressed the problem. The Judd EV's electrical ancillaries also generated failures, with occasional piston and valvegear issues adding to the tally of retirements.
Despite Capelli and Gugelmin scoring no points with the CG891, the team finished twelfth in the 1989 Constructors' Championship with four points. All four of those points came from Gugelmin's third-place finish at the Brazilian Grand Prix achieved earlier in the year with the older March 881.
The CG891 represented the first major expression of Newey's aerodynamic vision at a Formula One team, laying the conceptual foundation for the Leyton House CG901 that followed. The full-width diffuser and the extreme narrowness of the monocoque were ahead of their time and foreshadowed the approach Newey would develop through the 1990s at Williams and later at Red Bull Racing. The car's striking white, aquamarine, and blue Leyton House livery has become one of the most recognisable colour schemes of the late 1980s Formula One era.