Many of us will have driven a car that is powerful enough to spin its wheels as you change into second gear. Some may have been fortunate enough to drive a car that can produce a little chirrup as you do a full-bore upchange to third. But the new McLaren P1 goes further than that: if the road’s a bit greasy, it will spin its wheels all the way through fourth.

We’ve seen fast cars before. There have been Koenigseggs and Paganis, and the Ferrari F12 doesn’t exactly hang about. Then, lower down the food chain, there have been a selection of lightweight pocket rockets like the Ariel Atom and the Caterham R500. But we have never encountered anything quite like the P1. This takes our perception of speed to a new level.

My mate Niki Faulkner, who doubled as James Hunt in the movie Rush and has won many races in his time, emerged from a lap of Spa in the P1 wearing the face of a man who’s spent his life flying Spitfires. And had just been for a spin in the English Electric Lightning. He looked a little bit astonished. And if you peered into his eyes, which had been pushed round the side of his head, a tiny bit frightened.

Later, after my stint, I came into the pits with mildly soiled underwear and said to the team of mechanics: “I don’t want to sound pathetic or anything, but would you mind awfully taking that bloody thing out of Race mode.”

The trouble was that as I belted round, I’d been trying to deliver my pieces to camera, and I hadn’t managed to complete a single one without interrupting myself with a sudden, wide-eyed “******* hell”. “This car,” I’d say, “has a 3.8-litre, twin-turbocharged V8 which produces… ******* hell.” Then later, through Eau Rouge: “The feel of the steering puts me in mind of the feel you get from a Ferrari 458. It feels light and yet… oh, ******* hell.”

In Race mode, the car hunkers down by 50mm, and the rear wing grows into a slab that can generate 600kg of downforce. It’s supposed to make the whole thing grippier and stickier and more planted. But, on a wet day, it makes it feel nervous and skittish. And every time you go near the throttle, the instant torque of the electric motor kicks the back end out of shape. You have about four heart attacks and six adrenaline surges every 10 seconds.

In the rain, it’s better to leave everything in Sport. That way, you only have a heart attack every half hour or so. And yet. The previous day, I had been driving this incredible game-changer around the Belgian city of Bruges in electric mode. It had been silent and light, and the all-round visibility was good. It was a better urban car for these eco times than a G-Wiz. Mainly because, even with the petrol motor shut down, you still have 176bhp at your disposal.

So, to sum up the story so far. This is a car that can scare the bejesus out of a seasoned racing driver. It’s a car that can ruin every single piece to camera you try to make. And yet, around town, it’s Al Gore with a windscreen wiper.

This is because the P1 is a hybrid. It works on the same sort of principle as a Toyota Prius. However, unlike the Prius, you can go more than a yard in eco thrust mode. You can actually do seven miles before you need to engage that V8 generator. Then, you have a combined output of - stand by - 903bhp.

You’re scoffing, aren’t you? Because of course, the Bugatti Veyron SS has 280 more than that. Correct. But the Bugatti has four-wheel drive and weighs about the same as St Paul’s Cathedral. The P1, on the other hand, is rear-drive, and the only weight of any note comes from the air passing over the body.

The air is a major factor with the P1. The team behind the car say the entire body was not designed, it was engineered to manage the air, to smooth it down at the flanks, to use it to cool the brakes and to feed the chimney pot on the roof. And to help plant that rear into the road at speed. That rear wing, for example, is so big that as you go past 156mph, it lowers itself a bit or the downforce would be so great, it’d break the suspension.

Strange, then, that if you study the detailing carefully, you will notice that the McLaren Nike-style ‘tick’ badge is used everywhere. Headlights, bonnet scoops, flanks. Who knew it was so aerodynamic, I ask, with a little bit of a raised eyebrow.

Anyway, after pottering around Bruges for a day, I then engaged both engines and headed onto the motorway, where the McLaren continued to be two things at the same time. Fast and easy. First of all, because it uses the same sort of suspension set-up as the 12C, where none of the dots are joined up with anything more solid than a few volts, the ride is sublime. Citroen-from-the-old-days good.

It’s a doddle to drive as well. The gears change smoothly. The steering is super-light. If you shut your eyes, you could be in a squidgy wingback. What’s more, it is equipped with electric windows, climate control and satnav, which, in traditional McLaren style, doesn’t work. Sure, the carpets are an optional extra, but you can solve that by fitting them at no extra cost. And, at 80mph, the big engine can be a bit boomy. But you can solve that by turning it off and using electricity for a few minutes.

You’d imagine that, on a normal road, a car made from carbon fibre that’s unlacquered to save weight, military-grade aluminium and space-age ceramics would be about as relaxing as riding a tiger. But it isn’t. You could drive this car, easily, from London to India. You just have to remember to forget all you think you know when you press the accelerator. Because what happens when you do isn’t real. It’s from a world of sci-fi and monsters and fear.

We do a shot when we are filming TopGear. The camera car pulls into the inside lane and slows down. I then drop back and floor it, zooming past the camera in a blur and flurry of noise. We’ve done that with every car we’ve ever filmed. But you can’t do it in a P1 because if you drop back to a point where you are not visible and floor it, you will be doing 217mph when you pass the camera. That’s great television, but you wouldn’t be able to stop before you reached the traffic in front. So then there’d be an accident, and you’d have to go to prison.

Full throttle in a P1 is like Christmas. It’s something that you can only use once a year. And even then only briefly, because it actually hurts. When this car accelerates, it beats you up. It hurts your face. It’s like Christmas in other ways too. It causes arguments with your loved ones. And it’s great. Oh, and when you are going flat out, you can push a button marked DRS, which lowers the rear wing. This reduces drag and lets you go even faster. But when would you ever need more speed in a car that has 903bhp and less fat than Willem Dafoe?

There’s another button marked Boost. Push that and, weirdly, you lose around 150bhp. But it hasn’t actually gone anywhere. It’s all sitting in a big, spare power jar, and if you push a button on the wheel, it all comes back. I can think of no occasion when this would be useful. Except just after your passenger has crapped themselves, you can say: “Huh. You think that’s fast? Watch this.”

It’s strange, though, isn’t it? McLaren has always been the most anal of the F1 teams. Nobody has ever dropped into its big grey motorhome for a giggle and a natter. And yet here is a car that has Boost and DRS features that are fitted for… fun.

I’ve never been a fan of McLaren’s road cars. I always hated the F1 and didn’t really buy the argument that its engine bay was lined with gold because that’s the best heat-resistant material. Interestingly, they tried to use gold in the P1, but it failed the heat test.

Then there was the SLR, which was a Mercedes SL with rubbish brakes and a silly pricetag. And then there was the MP4-12C. A very good car, but a bit clinical. And that name was stupid. Though it’s not as bad, if I’m honest, as P1. It’s just so knowing. So ‘in’. I hate it when the commentators say P1, when they mean ‘pole’, and I hate that McLaren has used it too. Especially as their cars haven’t actually been on pole since, er, they started working on the P1.

Everything else about this car, though, is either very brilliant or stratospherically brilliant. I love the way McLaren’s hijacked green hybrid technology and used it to create more speed. I love the way it all worked. I love the underlying British sense of humour and, with that back wing up, I love the way it looks.

It sounds pretty meaty, as well. Like a docker clearing his throat before eating a crane. The speed? Yes, I know I said the Ferrari F12 had gone beyond reasonable boundaries, but that thing’s a road car designed to be used by the owners of carpet warehouses in Huddersfield. The P1 is more of an event. An engineering boasting book. A thumb to the nose and four wiggled fingers in the general direction of those who thought we might have reached the outside of the performance envelope.

I have no doubt that the forthcoming Porsche 918 and the Ferrari TheFerrari will be fast and intoxicating as well. But I will be staggered if they are better than McLaren’s giant leap for mankind. I really will.

Pictures: James Lipman/Justin Leighton

The feature first appeared in Top Gear magazine