The most remarkable element of the way that the 12C drives is not its handling but the ride comfort allowed by its hydropneumatic suspension. The P1 utilises a similar system, but there’s no question that it feels set up to be firmer and more controlled.

However, the P1 still stops well short of being crashy or harsh, and it adeptly softens the edges to ridges and bumps. The suspension can be raised by 30mm to clear kerbs, too.

McLaren has created a car that is as joyful and as faithful to throw around a circuit as a kart

So there are plenty of cars with lesser performance that would feel less at home on a transcontinental drive.

Only the P1's noise levels become wearing on a long journey. It is reassuringly stable, solid and refined, with steering that, at 2.4 turns lock to lock, is far less nervous than the rack in an F12.

On give-and-take cross-country roads, the P1 has more performance and capability than you can use, given visibility and the laws of most countries. One of the challenges faced by modern performance cars, therefore, is to offer driver rewards at merely sensible speeds, and the P1’s ability to cover ground and engage its driver through linear, responsive controls and with strong feedback does precisely that.

And then you come to what the P1 can do on a circuit – and that is, quite frankly, astonishing, regardless of what you do with the chassis settings.  It’s good in all of them, but moving from Normal to Sport tightens the damping, and going to Track does so again.

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Hold down Race mode, however, and the P1 lowers itself by 50mm and raises its rear spoiler to its tallest, highest-downforce setting. Dropping itself increases spring rates by 300 percent, and the P1 behaves like a racing car.

It’s not the urge with which the P1 throws itself down the straights that is most extraordinary, or the fantastic power of its stoppers, or the outright grip, but its blend of all-round capability. That was the aim, says chief test driver Chris Goodwin: not to major on any particular area, but to excel in all.

Around our challenging dry handling circuit, a Veyron Super Sport demolishes every single corner exit and straight, a Caterham Seven 160 is astoundingly agile, a Radical SR3 SL produces race car levels of downforce and so corners with more speed than you thought possible, and a Toyota GT86 is playful beyond compare.

The P1 mixes elements of all of those – not to their extremes, but as a whole it eclipses them all. It scarcely seems possible, but McLaren has created a car that costs £866,000 and produces 903bhp yet is as joyful and faithful to throw around a circuit as a two-stroke kart.

When it came to handing back the keys to the Ferrari F12, it was with mild relief that we stepped away from it in one piece with sweaty palms and a time in the bag. In the more expensive, more powerful, mid-engined McLaren, we were disappointed that we couldn’t have stayed out there all day, chipping a tenth here and there in what is a brilliantly communicative, faithful and adjustable car.

The P1, unlike just about every other car of vast power, has no limited-slip differential. What it does get is ‘brake steer’, effectively an extension of the stability control that brakes an inside rear wheel on corner entry to decrease understeer and increase the turn angle. It is surprisingly effective.

It’s easy to adapt to the lack of a limited-slip diff because of the P1’s roll stiffness and its mammoth power and instant throttle response, which can quickly push the car into oversteer at the exit of almost any corner.

Stability control intervention gets freer as you flick through Normal, Sport, Track and Race modes, to the extent that you’ll hardly know it’s operating in Race. You can turn it off, but it hardly seems worth it, given that it’s so unobtrusive.

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The P1 is astoundingly reassuring at its limit. You can brake into a bend to unsettle the rear and get back on the power to ride out a slide with the same abandon as you might in a two-stroke kart. And you’ll want to do it all day. That is the P1’s greatest achievement.