Press the button labelled ‘Start’ for a few seconds and the XKR-S snorts into life before settling to a melodic and soothing thrum.

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Jaguar says the XKR-S Coupe is the quickest model in its illustrious history, but it’s still a cosy thing to drive at low speeds. Its leather seats adjust in 16 different ways for heaven’s sake.

It’s the same story with the Jag’s automatic gearbox, which might not be as quick-shifting as some newer rivals from the likes of Ferrari, but allows you to lope more serenely during the boring driving we all encounter most of the time.

And yet, this ‘cosy’ car can reach a top speed of 186mph and accelerate from a standstill to 100mph in 8.7 seconds, all while emitting one of the best exhaust bellows found behind a steering wheel.

To see it happen from outside you’d think the world had gone into fast forward.

At its heart there’s a 5-litre supercharged V8, which sends a prodigious 542bhp and 501lb/ft of torque to the rear wheels. This might sound like a recipe for nothing but smoking wheel spin, but during our drive – admittedly in the dry – the 295/35 R20 rear tyres and suite of electronic driver aids kept the XKR-S stable and fast, with little intervention to spoil the fun.

Its steering is light but accurate, and because the XKR-S is a long car, stability is excellent as you carve from one corner to the next. Gently feed in the power during a long gradual bend, and the cornering forces it can summon are up there with most supercars.

This is in part down to its adaptive damping system, which alters the setup of the chassis second-by-second and has been re-programmed to summon even more grip than in the standard XK.

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Exterior changes have been dictated by the wind tunnel, with new front air intakes, side sills, rear diffuser and rear wing all designed to take the svelte Coupe and improve its performance and high-speed stability, reducing lift by as much as 26 per cent.

20-inch gloss black ‘Vulcan’ alloy wheels and a 10mm drop in ride height visually plant the XKR-S onto the tarmac; just as well as its wings literally stick it to the ground.

Some feel these go-faster add-ons have spoilt the XK’s graceful lines, but as looks are purely subjective, we’ll let you decide. It certainly adds a dose of aggression, and takes on quite a different character depending on whether you go for French Racing Blue, British Racing Green, Italian Racing Red, Polaris White or Stratus Grey.

More likely to be off-putting is an average fuel economy of 23mpg, but in reality, the XKR-S is neither a car which is likely to be used every day, or one purchased by people too bothered about saving money at the green pump.

So, onto our final question. Who will buy the XKR-S? It’s less of a techno-fest than the Nissan GT-R and less well suited to track days than a stripped-out Porsche 911 GT3 RS.

We think it will appeal to buyers who want to experience the drama and performance of a supercar, but with fewer of the costs and frustrations of a mid-engined, carbon fibre exotic.

By Andy Goodwin, senior road tester, AutoTrader.co.uk