I was starting to think I shouldn’t have worn shorts and a scruffy T-shirt saying “Burnout king” to drive the world’s fastest and most expensive production convertible. Now I’m next to the gleaming silver wedge of billionaire boy’s toy, it feels a bit disrespectful. People who drive cars such as this don’t look like me. They have cashmere underpants and yachts made of ivory. That is the kind of person in the market for a £1.2m Bugatti Grand Sport.

Absorb that figure. One point two million pounds. For a car. Can it possibly be worth that much? Well, it is a serious piece of kit. Bugatti will make just 150 Grand Sports for people who think the coupé is a bit wallflowery. People rich enough to be able to afford a premium on the standard Veyron’s £880,000 and vain enough to want to be seen to afford a car quicker than many aeroplanes.

So the Grand Sport comes with a lift-off transparent roof panel and the same engine and transmission as the standard Bugatti Veyron 16.4 — a W16 motor with four turbochargers, four-wheel drive and seven-speed double-clutch transmission. The numbers are enough to make Ferrari and Lamborghini owners choke a little: 987bhp, 0-62mph in 2.6sec, 252mph. This thing will outdrag an Formula One car, spit on a Le Mans racer and laugh in the face of anything short of the space shuttle. This is not a mode of transport; it’s a physics experiment.

One thing it’s not is pretty. The Grand Sport is much smaller than you might think, but also squatter and squarer. It’s too bulky and muscular to be described as lithe or graceful. It has a slightly higher windscreen than the standard Veyron, and little tweaks to the LED daytime running lights and the air vents on top of the passenger cell, but with the roof in place you’d have to be a committed Veyron-spotter to tell the difference.

The roof, incidentally, is made from plastic — polycarbonate, technically — and you have to leave it in the garage if you want to scorch your forehead. Not the most elegant solution, even if there is an umbrella-cum-tent arrangement in the front boot that you can origami over your head if you get caught in a downpour. It’s supposed to be styled and inspired by the brollies that Bugatti racers used in the 1920s, but really it just looks like an expensive gazebo.

Thankfully, the rest of the engineering is a bit more 2020 than 1920. Removing the roof from a car — especially one as powerful as this — is a complex business affecting everything from structural rigidity to balance and safety. Think about it — you’d be wobbly if someone removed the top third of your spine. So, in an effort not to embarrass oligarchs, sultans and bosses of telecoms companies, the Grand Sport has been modified. That means the monocoque skeleton has been beefed up around the side-skirts and A-pillars, the B-pillars behind your head have been stiffened and a big carbon plate has been bolted under the transmission tunnel to stop the car from flopping about like a wet cardboard box. Apparently the Grand Sport suffers less twisty flex than any other roadster ever.

The car is easy to get into and see out of — forwards, at least. It’s massively wide, though, and the rear view is obscured by that humpbacked shape, although reversing is helped by a 2.7in monitor in the mirror linked to a camera on the back of the car.

Like the hard-top Veyron, which was designed to be as much an everyday car as a supercar, the Grand Sport is easy to drive. Even the double-clutch DSG gearbox is user-friendly. You slip the lever into “D” and potter away either in “auto” mode or flicking daintily between gears behind the steering wheel with your first two fingers. There’s no transmission jerk, no overwhelming sense that this is a vehicle that needs 10 radiators just to keep itself from exploding. It’s as easy to drive as a Volkswagen Golf.

Sort of. Because I’ve never driven a Golf that has rendered me incoherent. After I’ve been “assessed” by a professional driver for a few miles, my chaperone leans in, tells me to drop a couple of gears and floor it. There’s a slight pause as the car gathers a breath . . . and then the world changes. The power meter underneath the rev counter swings around to maximum, the Grand Sport squirms and, drawing on years of journalism, wit and erudite banter, I shout: “AAAAARGLE!” When you remove foot from throttle, the sound is like a rumble of thunder directly behind your head. Nothing on God’s green earth comes close.

I’ve driven dragsters that match it for off-the-line punch, but they fall over when faced with a corner; the Veyron flicks towards the apex and shrieks its way around pretty much anything bar a hairpin at speeds that make your hair fall out. I would not have been surprised if we’d got out and the tyres had been replaced by pitons, and the engine had turned into a jet turbine. It doesn't just grip; it digs. It doesn’t just accelerate; it punches the horizon through the back of your head.

The Grand Sport has slightly softer suspension than the coupé, the factory in Dorlisheim, Alsace, reckoning that most convertible buyers will be keener on cruising, but I couldn’t tell the difference. The car weighs nearly two tons but feels half the weight. It changes direction like a housefly.

The one big difference is that in the Grand Sport you hear far more than you do in the coupé. It’s almost reason to shell out the extra cash. The noise wobbles your brain until your eyes go blurry and the world loses its varnish. The exhaust note in third gear at full pelt makes you want to duck.