The car was designed by Frank Dernie and Nigel Stroud and was the last car built by the Hesketh team before it folded at the end of 1978.

The 308E was a relatively conservative design, with an aluminium monocoque chassis built around the common Cosworth DFV engine and Hewland gearbox combination.

However, the 308E gained particular notoriety owing to Hesketh's team sponsors in 1977 – Penthouse and Rizla – and the resultant livery which incorporated a large rendering of a scantily clad Penthouse Pet embracing a Rizla packet.

During this year, driver Rupert Keegan managed to qualify the car at every race entered although its best finish was only seventh place at the Austrian Grand Prix.

For 1978 the team reverted to rather less controversial sponsorship from the Olympus Corporation, although results were less dependable.