Owner Frank Sheach’s shiny red 1981 Mark V doesn’t even have a number plate, because it was never registered.
The classic car buff has kept his mint condition Cortina under lock and key — only transporting it to shows on the back of a truck.
Last night Frank, of Dundee, said: “I’m going to give someone else the opportunity to own a piece of history.
“It’s the only one I know of that hasn’t been driven. There is only delivery mileage on the clock and it’s brand new.
“I bought it seven years ago and although I wanted to drive it I’ve resisted it.
“Since then I’ve taken it round car shows but you can only do so much of that. I’ve decided to auction it off. But I’ve no idea what it’s worth.”
Frank’s 2.0-litre GL motor would have cost £5,500 in 1981 — about £19,000 in today’s money.
He told how the car was first bought new by multi-millionaire enthusiast TC Harrison who kept it in his collection until he died.
The iconic Cortina was the best-selling car of the 1970s, shifting more than a million of each of the five models. Mark V prices started at around £3,500 for the basic 1.3-litre engine.
A brown 1974 Mark III was driven by Gene Hunt and sidekick Sam Tyler in the first series of BBC cop show Life on Mars.
Life on cars ... Gene and Sam
Detective Inspector Jack Regan often drove a blue Mark IV in the gritty 1970s TV crime drama The Sweeney.
The car’s name was inspired by the Italian ski resort Cortina d’Ampezzo, home of the 1956 Winter Olympics. As a publicity stunt, several were driven down its bobsled run.
The last Cortina — a silver Crusader — rolled off the production line at Dagenham, East London, on July 22, 1982. It was replaced by the Ford Sierra.
Describing his car, National Express engineer Frank added: “Anybody buying it can choose their own number plate if they want to register it.”
But he reckons if it were to get a standard reg, the DVLA would have to give it an old-style 1981 plate.