For the time being it is, says McLaren, if not the fastest car in the world - that title almost certainly belongs to Ferrari's even more potent, slightly lighter LaFerrari - then the most exciting hypercar to drive the world has ever seen.
That's some claim when there are machines such as the aforementioned Ferrari and Porsche's breathtakingly brilliant 918 Spyder to compete with, but then McLaren has never been one to do things traditionally.
There will only ever be 375 P1s built, all of which, claims McLaren, have already found buyers. At its core, the P1 boasts a two-seater carbonfibre tub, much like that of a Le Mans prototype racing car.
It is propelled by two distinctly different power sources. The first is a twin-turbo 3.8-litre V8 engine that produces 727bhp at 7300rpm and 73.41kgm at 4000rpm. The second involves an electric motor that uses a brace of lithium ion batteries to produce a further 176bhp and 26.55kgm of torque. This provides the P1 with combined outputs of 903bhp and 91.8kgm of torque.
As you'd expect, the car is made from all sorts of exotic materials beneath its mostly carbonfibre outer skin, but the key statistic that results from their use is a kerb weight of just 1450kg. This gives it a power-to-weight ratio of well over 600bhp per tonne, and that, says McLaren, is enough to fire the rear-wheel-drive P1 to 100kph in just 2.8sec, to 161kph in well under six seconds and to 322kph in under 20sec.
Bear in mind that when we tested the F1 all those years ago it recorded times of 3.2sec to 100kph and 6.3sec to 161kph, and you begin to get some idea about how monstrous the P1's performance really is.
And that's before you so much as mention its actively managed, hydraulically controlled aerodynamic package, its vast retractable rear wing, its super-fast dual clutch gearbox, its carbon ceramic brakes and its phenomenally clever traction and ESP systems, none of which were present on the F1 but all of which, says McLaren, make the P1 faster - in some cases a lot faster - than it would otherwise be.
Fast enough to lap the Nürburgring in "considerably less than seven minutes" says McLaren.
I drove the P1 first on the roads in and around the circuit of Bahrain, and then on the GP track itself, albeit for just a few brief laps. On the road, the first impressions are of a car that feels remarkably like a McLaren 12C. Which is either a good thing if you've never driven a 12C before or, initially, a mild anti-climax if you have.
The driving position and cabin architecture are both instantly familiar while the driver's seat - though more supportive than a 12C's - clamps you in position in exactly the same way, behind a steering wheel that is again different in its detail design but which looks and feels familiar.
The longer you spend behind the P1's multi-adjustable wheel, however, the more obvious the differences between it and its baby brother become. There are, in fact, lots of extra buttons on both the dash and the steering wheel, many of which control the car's hybrid system but also its "push to pass" feature and Drag Reduction System when in Track Mode.
There's also an extra depth of sound from the twin turbo V8, even when you give it just the gentlest of prods in a high gear. Likewise, the dual clutch gearbox feels snappier and more responsive in all of its various drive modes.
And best of all, again only to begin with, is what happens when you press the "E Mode" button on the dash. The moment you do, the V8 dies and you are left with the spooky but rather wonderful realisation that you can drive the P1, all 903bhp of it, while making no noise whatsoever. You can't do that in a 12C.
The P1 is not ultimately a car to be driven slowly, however, even if its electric power source does provide it with a hit of throttle response that a straight turbocharged car couldn't hope to replicate. Instead it's about going fast - really, really fast - and this is something it can do with varying degrees of madness depending which mode you choose to drive it in. Which probably sounds a little bit digital but which is, in practice, anything but.
What the car's various drive modes allow you to do is build up gradually to a point where you can begin to work out what it can do ultimately. Were you to just stick it in Race Mode and let rip, I'd say 90 percent of even quite competent drivers would fall straight off on the first lap. The P1's potential to reach the horizon that much quicker than you imagine really is that great. Initially, the car is pretty hard to get your head round.
So, I drive it first on the track with the chassis set to normal and the powertrain set to track, and the boost system switched on. This gives the best throttle response and the quickest reactions from the gearbox but cuts power back to a mere 727bhp (pah!). In order to summon the full 903bhp you must press the iPAS (push to pass) button on the steering wheel, and you do that only when the car is pointing straight.
Out of the pit lane and on to the circuit proper, the P1's ride feels sporting but well damped, stiff but still compliant. The steering is light but super precise, much like that of the 12C, and the brake pedal feels deliciously firm underfoot, the stopping power total. Unlike Porsche and Ferrari, McLaren decided not to harness power to the batteries with regenerative braking because they wanted maximum feel through the pedal, at all speeds, and it shows from the very first time you hit the pedal.
Through the first few corners taken at speed there is no perceptible body roll but, instead, just lots of bite from the front end via the bespoke P-Zero Corsa tyres, with a correspondingly faithful reaction from the tail.
The first time I pedal it hard out of a corner, the rear tyres light up and the thing takes me completely by surprise. I actually think I'm about to turn it right round. But then the traction control does its business and saves me, and after that first hit, after that first glimpse into the monster's eyes, I learn to regard the P1 in a very different light indeed.
This is not, I rapidly conclude, a Big Daddy version of the 12C. It's a completely different animal. One that will chew you up, take you for a death roll for a while, then spit you back from whence you came. And that's in Normal Mode.
In Sport and Track Modes, the chassis responses get that little bit crisper, the steering that little bit more incisive, but to be honest, the differences are subtle. In Race Mode, well that's an entirely different prospect.
Because if you think the P1 feels like it's dialled up to 11 in Track Mode, in Race Mode, it goes to somewhere on the far side of 20. It feels like a totally different car as a result.
So what is it about Race Mode that transforms the P1 so dramatically? For starters, the ride height automatically drops by 50mm. That enormous rear wing also deploys so that you get a vaguely hilarious 600kg of downforce at 241kph. And on top of that, the suspension goes up at least two notches on the stiffness and response scales while the engine, if you deselect the boost function, delivers the full 903bhp and 91.8kgm all the time, and seemingly at the merest twitch of your right foot.
The corresponding leaps in performance, cornering grip and dynamic clarity are, shall we say, quite impressive. And they were already pretty mind bending in the first three "ordinary" modes.
With Race selected, the P1 feels completely unhinged in a straight line to be perfectly honest, faster than any other road car I've driven by some margin, including a Bugatti Veyron Supersport.
But it's in the corners and under brakes, and at the corner exits, that the P1 feels even more other-worldly. The grip it generates through fourth gear corners and above is frankly ridiculous for a road car, and the way it stops from high speeds is enough to make you feel slightly unwell if you're not braced for it.
And, best (or worst) of all depending on how brave you're feeling, it will also allow big hits of opposite lock before the ESP or traction control systems intervene. You feel a lot more on your own in the P1 than you do in, say, a Porsche 918 on a track. More than any other characterstic, perhaps, this is what separates their personalities.
Should you buy one? If you can afford it, you can probably guess the answer to that now. But, unfortunately, you can't now because all 375 P1s have already found homes.
So maybe the more relevant question is - should McLaren have built more than 375 examples in order to generate a bit more profit from the project?
Hindsight is a wonderful commodity, and in light of what happened to initial F1 sales, which bombed back in the 1990s, no one is going to blame McLaren for erring on the side caution when it comes to build numbers. Especially not when they have created such an extraordinarily brilliant car.
The P1 deserves all the success it gets. It is, for the time being, the most exciting car to drive in the world.