Like the 308B that preceded it, the 308C featured a narrow front end tapering out to wide, low sidepods, with the main radiators positioned ahead of the rear wheels. The rubber suspension was inboard and operated via rocker arms — Postlethwaite's signature engineering approach first developed for the 308 family. The DFV V8 remained the power unit, as was standard practice for independent teams during the period.
The car was introduced late in 1975 for James Hunt and made its race debut at the Italian Grand Prix at Monza, where Hunt finished fifth. At the season's final round in the United States, Hunt brought the car home fourth.
At the end of 1975, Lord Hesketh could no longer finance the team's unsponsored campaign and withdrew from Formula One. The 308C's next chapter came when Canadian oil businessman Walter Wolf bought 60 percent of Frank Williams Racing Cars ahead of the 1976 season, forming the Wolf-Williams Racing partnership. Wolf simultaneously acquired the assets of the disbanded Hesketh team, including the 308C chassis, which was rebranded as the Wolf-Williams FW05.
Harvey Postlethwaite, who had designed the car, joined Wolf-Williams as chief engineer — maintaining continuity between the Hesketh programme and its reincarnation in Reading under the Williams banner.
The Wolf-Williams FW05 made its debut at the 1976 Brazilian Grand Prix with Jacky Ickx driving. The team also ran the Williams FW04 (briefly rebranded as the Wolf-Williams FW04) for Renzo Zorzi at that opening race. From the second round onward, the team operated two FW05 chassis.
The FW05 struggled throughout the season. Ickx and his various teammates — Zorzi, Michel Leclere, and Arturo Merzario in turn — rarely made strong progress against the more advanced machinery being developed by the leading constructors. The car was eventually found to be overweight, which compounded its competitiveness problems.
Notable incidents during the season included the German Grand Prix at the Nurburgring, where Merzario stopped the Wolf-Williams and ran to help extract Niki Lauda from his crashed, burning Ferrari — an act of bravery for which Merzario was widely recognised. At the Italian Grand Prix, a complex chain of qualifying disqualifications and withdrawals involving fuel irregularities reshuffled the grid in unusual circumstances, but neither Wolf-Williams driver benefited significantly.
Ickx was released from the team mid-season after failing to qualify in Britain and was replaced by Merzario. Chris Amon joined for one race in Canada but was put out by a collision at the start. Warwick Brown took over for the United States Grand Prix East, and Masami Kuwashima was announced for Japan before his backing collapsed and he was replaced by Hans Binder. Both Merzario and Binder retired in Japan.
At season's end, Wolf restructured the team by removing Frank Williams from his management role entirely. Williams, disillusioned by the arrangement, departed and established Williams Grand Prix Engineering with Patrick Head in 1977 — the foundation of one of Formula One's most successful constructors. Wolf took full control of the team, which became Walter Wolf Racing for 1977, fielding entirely new machinery.
The 308C's career thus spans two distinct lives: a late-1975 cameo under the Hesketh name that showed the car's basic competence, and a full 1976 campaign under Wolf-Williams colours in which it served as a transitional design during a period of institutional upheaval. It is remembered primarily as the chassis that bridged Hesketh's departure and the early days of what would become the Williams organisation.