In a world of iPhones, Snapchat, Pokemon and a whole host of digital distractions, do little boys and girls still put posters of supercars on their walls? It's a question we're musing as we drive the new McLaren 720S around the Cirencester bypass. Growing up in the 80s, the most coveted supercar poster was the Lamborghini Countach. What made the Lambo shocking was its scarcely credible design. It was low, it looked like a wedge of cheese with wings attached – as it had doors that opened up toward the sky. It was enough to make any eight year old go all open-mouthed.

So can McLaren's latest supercar do the same, in the here-and-now of 2017? From our time behind the wheel, signs are good. Even in its milky off-white hue, the 720S attracted significant attention – within minutes of each other, a group of lads in a Peugeot, a businessman in a BMW SUV and a white van man all give chase, whip out their camera phones and then give the thumbs up.

Want to get noticed? The 720S does the job. And then some. Want to escape the paparazzi? Well, in a 720S that's just a single flex of your foot away…

McLaren makes supercars, pure and simple. It's a firm that's built on a reputation built in Formula One racing. So no McLaren is slow. But what's it like to drive this – the fastest, current production McLaren – on the road? In a few words: mind-alteringly staggering.

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The McLaren is in the "silly fast" car category. In a (merely) fast car, you look at overtaking opportunities as just that – your brain asks the question "have I enough road space and time to get past?". You think about it. Use judgement. As you spend time in the 720S, your brain learns to skip out this thinking step. It doesn't matter how short a piece of road you have, there is almost always time to get past a slower moving car. Simply plant the throttle and, zoom, you're past.

The numbers feel largely irrelevant – but are worth writing out for the record: 62mph from standstill comes up in 2.9 seconds, while 124mph (a nice round 200 km/h) takes just 7.8 seconds. The 720S will do 212mph. Practically, this means that you never plant your foot in this new McLaren for more than a couple of seconds. Do so and you're risking jail time. Above 5,000rpm particularly, the engine makes the McLaren feel utterly savage. You're holding on, even with electronics systems engaged, trying to stop it throwing you off the road. If you feel the need to go faster, you're going to need to leave the planet (may we suggest one of Mr Musk's nice rockets?).

That performance is all well and good, but given we have to drive within a world filled with speed limits (yes, we know, how annoying), isn't a supercar's appeal mostly about raw emotion, looks and posterchild appeal? Previous McLarens haven't ticked that box. They've been seen as a bit dull. But while the 720S has difficult angles, and isn't beautiful in a conventional way, it is visually arresting.

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The body volume is complex, with wild scoops and floating sections, all in the name of aerodynamics. The cabin section is mostly glazing. And then there's that controversial front: the headlamps are actually recessed into a scooped away black volume – almost like an eye socket devoid of eye-ball – with slim LED bar poking out, giving the McLaren an otherworldly, mechanoid expression.

With this car, we think McLaren's design language has gone from the dullest and workaday of the supercar brands (Ferrari, Lamborghini and Porsche), to the most expressive and arguably interesting. Whether you like it or not, it's hard to argue with the fact that McLaren has established itself as a genuine, credible competitor to a Ferrari or Lamborghini. Some feat for a car company that is only seven years old.

The 720S represents a milestone for McLaren – and a significant risk. It's the firm's new Super Series model (the cheaper, less powerful Sports Series cars are represented by the 540 and 570), and it's called 720 because that's how much power it produces. It replaces the 650S – itself a modified 12C, which was originally named MP4-12C – which was the first car McLaren cars produced. See, not confusing at all.

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But second-generation cars are a little bit like difficult second music albums. The first-gen product always gets the benefit of the doubt. It finds media who welcome something new, and often turn a blind eye to faults. And owners who are happy enough to be glorified beta testers. We could mention Tesla here… which would be unkind to McLaren.

So there's a weight of expectation on the 720S, because it needs to improve on the very capable (but a little bit dull) 650S. It needs to be able to appeal to people who'd otherwise buy a Ferrari or Lamborghini – not only on raw numbers, but emotional appeal, too. Call it the bedroom wall poster test.

Getting inside is, as with all McLarens, half the fun. There's no conventional door handle, while the door itself appears to have two skins (there's basically an aero channel running within the door). Drop your hand into the gap, feel for a pad on the inside edge and the door clicks open. It then lifts up, in an arc which swings it up to the sky and forwards towards the front wheel – hinging from a point in the middle of the roof, taking a chunk of the roof away with it. Dramatic entrance? Very much so. Just don't attempt to get into a 720S in a crowded car park.

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Step inside – which easier than in any McLaren before, because the high sill of the carbon tub has been reduced – and you're greeted with an interior that's impressively bespoke. Unlike some super car makers (looking at you Aston Martin), you won't find things like the window lifters from a Ford, or an infotainment system from a Mercedes in here.

Stretch back up to pull the door down – remember, it's going to literally put the roof back over your head – and instead of making you feel claustrophobic, like many supercars do, it's striking how light this cabin is and how good visibility is.

The carbon fiber structure has allowed ultra-slender pillars, while glazed elements in the roof and rear C-pillar area mean you're literally surrounded by glass. At first, it's like you're in a goldfish bowl. The reality is it makes the McLaren easy to drive because it's easy to position on the road. And it creates a heightened sense of speed and sense of yourself in space.

As for performance, well, we've already hinted at what's possible. But part of what makes the McLaren special is that unlike many super-fast cars, – which only come alive and feel really fast when you drive them at speeds which are silly – the 720S feels unusual even when you're doing less than the speed limit.

It's to do with where you sit, and that cabin glazing. You're low in the car, fairly central and quite far forward. But the glass line comes low, so the view out is great. Which heightens the sense of speed and makes the McLaren feel involving and fast, even when you're not tanking along. It's almost like the roof's off, or you're having your sensory perception of outside altered by the car's design.

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If this sounds like gibberish, we'll try to illustrate the point by saying that, while driving along one road, an arc of leaves swept up from the car in front, and as one leaf came directly towards our McLaren's windscreen, we instinctively ducked, because it felt like that leaf was about to make direct contact with our head.

Don't underestimate the McLaren as some shy and retiring type that can't do the numbers though. It's utterly nuts if you want to let it off the leash.

However, the best aspect of the 720S is not how fast it can travel, but how it moves down a road dynamically.

The steering is beautifully weighted and reactive, it's quick to respond, but not so it feels hyper and darty like a Ferrari, rather that you can immediately take confidence in what the car is doing. It lets you know. And the body never seems to roll, you just throw it into a corner and it tracks perfectly, without barely any sense of pitch. It is, in some ways, like driving an oversized Lotus Elise. And that's the biggest complement we could ever pay it.

Despite all of this, in comfort mode at least, the McLaren rides over rough Cotswold roads better than the BMW 5 Series that took us to the launch event. Part of the trick here is the McLaren's adjustable drive setup, which separates the powertrain and the suspension – you've a choice to put either in comfort, sport and track – plus further selection to turn the stability system off, and put the automatic gearbox in full manual mode.

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Changes on that gearbox feel near instant – and McLaren's interlinked steering wheel paddles work intuitively and with a beautiful, short, sharp click. It's a 7-speed box and in auto mode the car is happy to trundle at very low revs in the name of economy. You'll not be surprised to hear that's not how we drove the McLaren though. Because its brakes are, in short, staggering.

It's perhaps unsurprising we were enthralled to the way the McLaren drove. It's one of the most powerful, sophisticated machines to ever hit the road. But the magic with which it corners, rides, and how useable this made it feel, combines with the cabin and seating position to make it feel pretty different to the Ferraris and Lamborghinis we've driven.

We got out wanting to get back in and drive it to John O'Groats. It feels like it has so much more to give, so many aspects still to reveal. People criticised the first McLarens for being one-dimensional and aloof. The 720S is nothing like that.

The tech on-board generally augments, rather than distracts from, the experience of driving a 720S. It doesn't feel like an old-school, tech-free car. Instead you're given a few key knobs and switches to adjust the drive. It's easy to simply slip a hand off the wheel and adjust these without distraction or much excess thought.

The gauge cluster you look at behind the steering wheel plays its part here. It's a visible screen when in comfort and sport modes, but flick into track mode and the screen tips forward and folds itself into the dashboard, presenting you with a slim display that sits in the end-on section of the screen.

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In this (race mode, effectively) you get a digital speed display, linear rev counter and gear selection displayed – and that's it. And as a way of conveying you the minimum amount of info needed, and not distracting you from the task at hand of driving, it works well. We preferred it to the slightly crass graphics of the main panel, which lack the fidelity or design quality you'll find from a large car maker like Volkswagen.

The portrait centre touchscreen simply does the job – it's not the most advanced, largest, highest-resolution display and it sometimes feels a little unresponsive. Whether you think it's the sort of system that should grace a £200k supercar is another question, but it is far better than what you get in a Ferrari or Lamborghini from a usability point of view, and the navigation system managed to keep us on track despite our somewhat deliberate attempts to get lost.

Other niggles? The driving position feels slightly offset, while the luggage deck behind the pair of front seats acts as a bit of an echo chamber, so the McLaren is not the most refined. But it's a supercar, not a limousine, so if you're looking for the latter then you're in the wrong place.

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We suspect the biggest issue for potential customers will be the aural delights from the engine, or lack of them. Imagine getting a paper bag, putting it over your mouth and then sucking in through it (and your teeth for good measure). Yep, that's what the 720S sounds like when accelerating, below about 5,000rpm. At about 5000rpm, it really goes for it and the V8 comes alive, with a hard, metallic roar echoing through the cabin. There's still not much in the way of tunes from the exhaust on the move, though. Start up, with both systems turned to track mode is a different matter, though...

Are these niggles serious flaws, or elements that create character that was missing in previous McLarens? We'd err towards the latter. The overall package feels special, the driving experience is mind-boggling, and the car feels like it would be easy enough to live with day-to-day – there's even a Porsche-like front boot which will swallow a holiday case.

Verdict

Designing the perfect supercar is hard. Fierce brand loyalty, growing competition, conflicting pressures to increase performance and efficiency while providing more emotional appeal make the dream project of supercar building a potential minefield.

Seven years ago, McLaren stepped into it with a product that could hold its head high – if not beat – the established competition, notably from Ferrari. We suspect you'd have struggled to find an MP4-12C adorning an eight-year-old's bedroom wall, though.

In 2017, things look somewhat different. And we're pondering if we've just driven a McLaren which establishes a new supercar world order. At over £250K to buy – yup, you read that correctly, quarter of a million pounds Sterling – it's close to Ferrari's 488GTB in price terms. But in performance terms, it's closer to McLaren's limited-run P1 hypercar of a few years ago.

The 720S is, in a word, magical to drive. Ignoring the engine sound, anyway. But the kick is that to look at, and to be in, it holds greater appeal than any McLaren before it. In anyone's terms, that makes it an utter triumph, and a car which is more than deserving of its elevated place among the supercar ranks – as well as a poster on any eight-year-old's wall.