At the front there was a simple, unequal length, double wishbone arrangement while, behind, a lower wishbone layout used the driveshafts in place of the upper links. Look at the suspension of an XJ6 and you’ll find a not dissimilar arrangement. Coil springs replaced the torsion bars found on previous Jaguar racers and adjustable anti-roll bars were fitted at either end.

It is a shame that we were never able to see how such a formula would have fared in competition but, by the time the wheels of development had slowly run their course, it had been left behind, its 2478lb kerbweight leaving it hopelessly overweight. All we know for certain was that, in 1967, David Hobbs drove it around the MIRA Proving Ground near Nuneaton at an average speed of 161.6mph, claiming the then-fastest lap of a UK circuit.

We’re back at MIRA today, the track with which the XJ13 was associated at first and then, some years later, upon which it would become indelibly imprinted. Yet it isn’t Hobbs at the wheel but an unfeasibly sprightly septuagenarian with a flat cap and cheeky grin. This is Norman Dewis, 73, Jaguar’s chief engineer from 1952 until 1985 and the man who, one day in 1971, had his life saved by this car.

“It’s a day I’m not likely to forget It happened on January 20 at 3.50pm. The XJ13 had been in mothballs for some years after the project was cancelled but they decided to dig it out when we put the V12 into the road cars. We were only at MIRA to do some promotional filming, not for any serious running. I’d been driving around the banking slowly for most of the afternoon but the director said he wanted a few quick laps. I did two pretty close to flat-out and decided to do just one more before calling it a day. Coming off one of the banked turns, the off-side rear wheel, which takes all the load, just collapsed. I was doing about 145mph.

“The car started to leap up the banking but I managed to pull it away from the edge. Then I switched off the engine and, once it was clear that there was no more I could do and that there was about to be a fairly massive accident, I wriggled down under the scuttle and hoped for the best.”

“Sir William Lyons wanted nothing more to do with the car and the wreck sat under cover in a corner of the workshop until 1975”

The perhaps unwisely named XJ13 dug itself briefly into the soft earth on the infield and then flipped. Dewis remembers it went end over end twice before starting to barrel-roll. Three complete revolutions later it finally came to rest, a bruised but otherwise unharmed Dewis still firmly wedged under the dashboard.

“I just walked away from it. After that Sir William Lyons wanted nothing more to do with the car and the wreck sat under cover in a corner of the workshop until 1975, when the rebuild finally took place.”

A remarkable amount of the original car was saved. Despite the fact that the front and back of it were now missing, the vital central box section had withstood the impact well while the engine and gearbox remained intact. Once back to its original glories, the XJ13 was sent out as an ambassador for the marque, visiting the US and Australia and finding a permanent home in Jaguar’s Browns Lane museum. It has been back to Le Mans and, last year after a lengthy engine and suspension rebuild, was seen charging up Lord March‘s front drive during the Goodwood Festival of Speed.

The problem with the XJ13, says Dewis, is its rarity. “It’s not like a D-type where, if something breaks, you can simply fit another part. There are no spare parts for the XJ13. Every component that exists for the XJ13 is already fitted to the car. If a bit breaks or wears out, there is nothing to replace it. That’s why it doesn’t run that often…”

It’s running today, as anyone who was anywhere on MIRA’s massive facility could not have failed to hear. Despite being a car born in the era where at least some pretence to road legality was required (it has a speedometer, handbrake and enough room in the boot for a spare tyre) these rules did not extend to require sound-proofing. Each of the engine’s banks runs into a single exhaust, exiting in artful channels so as not to interrupt air-flow under the car. It makes an unsilenced D-type sound like a limousine.

Dewis shows me around the cockpit. It’s a proper two-seater, though you sit rather cosily close together. There’s disappointingly little space inside: I’d hoped that, without the need to accommodate an engine, there’d be a useful amount of leg room but, in fact, the cabin is considerably less comfortable than that of a D-type. Dewis is built like a jockey and slides in beside me with case. The steering wheel is disarmingly old-fashioned, a traditional wood rimmed alloy-spoked affair whose 14in diameter is only a little smaller that those of the front-engined racing jaguars. It sits low in the car and in line with the driver, if not the offset pedals.

Instrumentation is straightforward but, bizarrely, not a single dial sits in your direct sightline, all the gauges being bunched in a group to your left. Still, no one is likely to complain about a lack of information as all engine functions, from the temperature of the water and oil to the pressure of fuel and oil, are all precisely monitored.

Firing it up is simplicity itself. With no carburettors to prime, you simply switch on the ignition and flick the fuel pump switch. The entire car hums briefly as the twin pumps fill themselves with four star. Then you tap down once more on the ignition switch and wait for the explosion. With the Lucas injection doing its stuff, it doesn’t take long. At an 1800rpm idle, conversation with Dewis, sitting scant inches away, is by sign language.

The gearbox is easy as long as you remember that its sequential interlock system prevents you skipping gears. So if, for instance, the car was in fourth when it last coasted to a halt, it will not provide first until it has become briefly reacquainted with third and second. The gate is hidden behind a gaiter and the linkage less precise than Dewis remembers, making it all too easy to try and pull away from rest in third. When I did it, I knew my mistake the moment the racing clutch bit but, far from stalling, the big V12 simply revolved ever more slowly and then pulled away like a locomotive. Most modern road cars, with today’s electronics, would have baulked at such treatment and it says much for the torque of the 32-year-old V12 that it never even looked like being a problem.

On the move it is a beautifully easy car to drive. For those who fit it is a comfortable car too; swapping ratios is childishly easy and, because of the exposed pipes shuttling water to and from the front-mounted radiator, warm enough to keep you cosy on the coldest of race days despite the open roof. Clearly its designers had thought hard about how best to preserve not only the car but also its driver and the need to keep him functioning at his best for 24 hours. It was a lesson Ford learned and, if you talk to David Hobbs, he will tell you the GT40 was an easy, vice-free car, which allowed its driver the freedom to complete the job in a fit state.

Whether the XJ13’s on-limit behaviour is similarly sweet natured, I cannot say. I can tell you it is ferociously fast, absurdly so by the standards of today’s more conventional supercars and that the noise is as sweetly savage as any made by an ’80s Group C Jaguar though nothing like as musical as a contemporary racing Ferrari. Today, however, is not for slithering around the outer limit, tempting Providence in a place that has already come within a breath of claiming the life of this car and my passenger. Today is for soaking up the atmosphere and savouring a unique experience. Even so, it is almost more than I can manage not always to tread the throttle to the ground and feel what remains of its 500 horsepower hurl us down the straight.

Later, Dewis climbs into the driving seat and heads off for a few laps. He drives it faster and better than I despite not having been aboard for what he will only own up to being “very many years”. Dewis is more than just a retired engineer: he is as vital a part of Jaguar’s history as any of its racers and you can see it written all over the faces of the Jaguar people who have come to watch these legends work. Dewis was always the team’s reserve driver and when the hired hands brought their racers in and blamed the car for uncompetitive times, it fell upon Dewis’s shoulders to take the car out and discover whether the fault lay with driver or car. Like Rudi Uhlenhaut at Mercedes-Benz, he proved rather successful at going faster than the works driver.

He comes back wreathed in smiles, frustrated like me not to be able to go faster but similarly aware that the price of breaking any part of the XJ13 would be hideously high. For me, it was the best part of the day, better even than the privilege of being allowed my own short stay behind the wheel. There is only one XJ13 in the world, one place in the world in which it was driven truly in anger and one man in the world who knew both better than any other. Seeing all three back together once more was a simple and ceaseless delight.