It's 2006 and the phone at Nissan's Technical Centre in Cranfield is ringing. Nissan's UK PR department is on the line, asking if the Cranfield engineers would be interested in creating a go-faster version of the already potent Nissan 350Z for the Goodwood Festival of Speed. Absolutely, the engineers reply, very interested.

The result is the car you see in the pictures above. At first glance, it looks like a standard 350Z. Until you notice the aggressive bodykit, the huge air intakes cut into the front bumper, the updated brakes and the high-set rear spoiler. Then you open the bonnet and discover that resting alongside the standard 3.5-litre V6 engine is something new - a supercharger.

This is the secret of the 350Z GT-S concept: a supercharger that boosts the car's power from around 300bhp to 382bhp. It also drops the 0-60mph time from an already quick 5.8sec to 4.8sec. In other words, this 350Z is quicker to 60mph than a V6-engined Jaguar F-Type and only 0.2sec slower than a Porsche 911 Carrera.

To go with its extra power, there's a retuned suspension set-up and myriad other tweaks designed to turn the 350Z from a street racer into a true Saturday special.

Sitting inside the cabin, there's almost nothing to mark this 350Z out from the crowd. Nothing, that is, apart from a small switch on the centre console that activates the supercharger. With the switch firmly on, the engine note changes from loud to downright deafening as the supercharger whistles into action. Set off, and the extra power on offer is intoxicating.

This feels like the natural evolution of the 350Z. It's glorious to drive quickly, and even though you can opt to turn the supercharger off, we dare say you might as well remove that choice. With so much power available, this 350Z does lurch forward at low speeds and, despite Nissan's work on the underpinnings, the ride remains firm but the GT-S concept is still amazing fun to drive. On the motorway, it's surprisingly comfortable and refined, too.

Perhaps the saddest thing here is that there is only one GT-S concept, and it lives as part of Nissan's own fleet. By the time it was revealed at the Goodwood Festival of Speed in 2006, the 370Z was only two years away and, despite rumours to the contrary, Nissan says there were never plans to launch the 350Z GT-S concept as a limited-run special.

So often with concept cars, you can see the business decisions for not putting them into production. Some are just too outlandish and too impractical to exist in the real world. But the 350Z GT-S isn't one of those cars. For once, I wish this was a concept that had made it to production, and I'm willing to bet it would have sold to the Z-car faithful by the bucketload.