The FW04 was designed by Ray Stokoe, a former McLaren engineer, and marked a deliberate break from Williams's earlier practice of running customer cars or designs produced by external companies. Frank Williams chose to build his own chassis for the first time, basing the FW04 on an evolution of the preceding Williams FW. The original FW had suffered from excessive body roll, so the new car was made considerably narrower and more streamlined, with repositioned radiators and fuel tanks intended to improve aerodynamic performance and overall handling.
A key appointment for the 1975 season was the hiring of a young engineer named Patrick Head, who would go on to become one of the defining forces at Williams. The FW04 encountered overheating problems and fuel pick-up failures early in its life, and Head redesigned both systems at short notice, substantially improving the car's reliability. Fina served as major sponsor, supplemented by funding from Ambrosium, a Swiss finance company.
The FW04 did not appear until the Spanish Grand Prix, partway through the 1975 season, meaning Williams continued running the older FW03 alongside it for much of the year. Arturo Merzario drove the FW04 on its debut in Spain but withdrew before the race, citing improperly secured barriers at Montjuich Park. Jacques Laffite subsequently became the car's primary driver, while various other drivers handled the second chassis on short-term arrangements.
The car struggled through most of the season. Laffite failed to qualify in Monaco, retired with gearbox failure in Belgium, and suffered further mechanical problems in the Netherlands and Britain. The one exception came at the German Grand Prix at the Nürburgring. Racing down in fifteenth on the grid, Laffite benefited from a race of attrition — mechanical failures, accidents, and punctures for rivals ahead — and was able to overtake Tom Pryce near the finish to cross the line in second place. It was the best result Frank Williams had achieved as a constructor to that point, earning six World Championship points and providing enough financial relief to keep the team running through the remainder of the season.
That Germany result was the team's only points finish of 1975. By the season finale at the United States Grand Prix, a second FW04 had been built, but neither car started: Laffite was unfit to race having qualified twenty-first, while Lella Lombardi, driving the new chassis, could not get away due to ignition problems. Williams finished ninth in the Constructors' Championship with six points, all scored by Laffite in Germany.
At the start of 1976, Canadian oil millionaire Walter Wolf purchased a 60 percent stake in Frank Williams Racing Cars, transforming the outfit into Wolf–Williams Racing. The FW04 was rebranded the Wolf–Williams FW04 and made one final Championship appearance at the Brazilian Grand Prix, driven by Italian newcomer Renzo Zorzi. Zorzi qualified seventeenth and finished ninth, outqualifying his teammate Jacky Ickx in the rebranded Hesketh-derived FW05. After that race, Wolf–Williams had two FW05s available and the FW04 was set aside.
Chassis "01" was sold to Australian privateer Brian McGuire, who entered it in the 1976 Shellsport International Series under the McGuire BM1 name after modifying the car. He won Round 10 at Thruxton, the first time a Williams-derived car had taken pole position and fastest lap in a race. McGuire also made a brief attempt to enter the 1976 British Grand Prix, which organisers rejected, and he later purchased the second FW04 chassis as well.
In 1977, McGuire continued to campaign the modified cars under the BM1 designation in the Shellsport Series, but the results were disappointing. During a practice session at Brands Hatch in late August 1977, one of the cars left the track and struck the barriers, killing McGuire and a fire marshal. The accident ended the FW04's competitive life entirely.
The FW04 occupies a modest but significant place in Williams history. It was the first car designed entirely within the team, the first to score a podium result, and the machine on which Patrick Head learned his craft before helping found Williams Grand Prix Engineering. The second-place finish at the 1975 Nürburgring was a turning point that gave Frank Williams the funds and credibility to keep building toward what would become one of Formula One's most successful teams.