The car gave Hunt and Hesketh Racing their only Grand Prix win together, at the 1975 Dutch Grand Prix in Zandvoort.
With 23 Grand Prix starts, 17 of which were driven by Hunt, chassis 308/2 is the last privately entered car to win a Grand Prix without commercial sponsorship.
Hunt moved to McLaren in 1976 and won the world championship in his first season.
Hunt's son Freddie has driven the car at Goodwood Festival of Speed events, and it has been campaigned by the current owner within Formula One Historic races, including at Monaco.
Silverstone Auctions' managing director Nick Whale has called the vehicle "a very important part of Formula One history". No estimate has yet been provided for it.
Classic car investors will also enjoy a £70,000-estimated 1970 Costin Amigo on offer at the same sale.
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