The news comes just days after it was revealed that Mr Meek, a prominent Leeds businessman known for his love of sports cars, had died.
The Costin Nathan will be sold by H&H Classics car auctions after it was discovered by a house clearance company in Manchester.
The company says the car may be worth £25,000 to £30,000 when it is sold at their Chateau Impney Hillclimb sale in the Droitwich on July 10.
Racing as both a Spyder and GT in period, the two-seater now requires total restoration. Appearing to be substantially complete, it is estimated to fetch £25,000 - £30,000 and comes with a highly prized Hewland MK5 gearbox and Ford-based Twin-Cam engine in pieces.
Despite its short career, the Costin-Nathan proved to be a very capable racer. Surviving examples showcase Costin’s unique talent for designing lightweight and very aerodynamic racers.
The car is the original works prototype as raced with considerable success by Roger Nathan in 1966. It was bought by the present owner, who has now died, in 1967.
Former racing driver, John Markey, who runs the H&H Classics Hindhead Surrey operation, said: “It is an amazing restoration project and a true ‘barn find’ slumbering in the late owner’s garage for the last 45 years.
“This is quite a special car.
“I’m probably dewy eyed having raced one quite extensively in the 1960s.”
The car was a collaboration between engineer Frank Costin and racer Roger Nathan. Work began in 1965 with the prototype making its debut at the following January’s Racing Car Show.
It was renowned for being light and fast. It had an aluminium body where its later production siblings used fibreglass.
The car, with Mr Nathan at the wheel, achieved success. The highlight was Mr Nathan’s victory in the Coupe de Paris in 1966.
It was sold to a G M Horsley in 1967 and Mr Meek was engaged as driver. The car had a more powerful Lotus Twin-Cam engine installed. However, various teething problems and some bad luck meant that the Works Prototype was never as successful in its revamped guise, but Mr Meek scored a further class win at Snetterton during 1967.
Retired after a few seasons, the Costin-Nathan remained in G M Horsley’s ownership and was stored in a barn.
Mr Meek, chairman of the Titan Group property firm in Leeds and the owner of the Mallory Park racing circuit in Leicestershire, died on Saturday, May 21.
Mr Meek, who was always coy about his age, achieved more than 500 race wins during a racing career covering Formula 2, Formula Atlantic, Formula Libre, Formula Ford, Formula 3, Saloons and GT cars. He was also seven-time production car champion.
His funeral will be held at St Anne’s Cathedral in Leeds on June 3.