DETERMINING the essence of Jaguar is not rocket science.

Obviously there is Britishness to consider, slinky designs to match the feline name, advanced technology as a reflection of the brand’s proud tradition, tangible high-quality craftspersonship, and persuasive yet contained performance.

Retro certainly isn’t part of a modern Jaguar’s repertoire but timeless elegance should be. Lounging room for four adults would be lovely but accommodation priorities really ought to focus on front-seat occupants. And comfort? A supple ride is paramount.

So welcome then to the 375kW, $367,800, 5.0-litre supercharged Supersport Long Wheelbase - the pointy end of what is only the fourth all-new XJ range since 1968.

By now you’ve probably heard enough about the exterior design that owes nothing to its predecessors – in utterly stark contrast to this model’s blatantly retro X350 predecessor of 2003.

Modernism of breathtaking ambition was obviously the latest XJ’s overriding brief. Divisive, discussed and never ignored, nothing on the road – not even the smaller, prettier XF sibling – looks anything like it. Bravo for boldness, Jaguar.

No such revolution is going on underneath, however. That happened eight years ago, for the archly conservative (but still beautiful to some eyes) previous XJ’s aluminium-body, space-frame construction, and computer-controlled air suspension are still tomorrow’s tech in most people's cars.

But in an ironic twist of the X350’s light literally hiding beneath a bushel, luxury car buyers couldn’t see the old Jag’s envelope-pushing advancements and so overlooked it almost wholesale.

Meanwhile, the newcomer’s cabin is somewhere between yesterday and tomorrow.

Even before setting foot inside, the first surprise is the sheer lightness of the doors. Aluminium, remember. It must be quite a challenge for Jaguar’s engineers to impart a sense of solidity when a door doesn’t shut with a bank-vault heft. You do get used to it quickly though.

We’re talking about the Supersport here – a model that, let’s face it, seems tailor-made for footballers, globetrotting DJs and Brit Award attendees as surely as for captains of industry. Hence the cocktail bar meets nightclub ambience.

Actually, perhaps Austin Powers provided inspiration for the purple velour glovebox and centre console upholstery.

And taking into account the voluptuous shape of the stitched leather dash-top, with its gorgeous chromed air-vents, images of Barbarella spring to mind. There’s sensual stuff both subtle and gross going on in here.

We won’t bore you with the rudimentary details – except that the utterly sumptuous seats are perfectly comfortable and ultra-adjustable for every-which-way positioning, to help enhance an already thoughtful driving environment.

Space to spread out is this car’s specialty as a result of the XJ L’s extended wheelbase, but we weren’t quite expecting this much rear headroom. The roofline does boast a coupe-like silhouette, after all.

Other surprises: touch-sensitive interior lighting and glovebox gorgeous piano-black trim rich leather upholstery chrome splashed liberally around knobs and levers suede-effect roof lining there’s an inescapable sense of being cocooned in Victoria Beckham’s handbag.

No old-school wood nonsense in here – though of course that is available should you so desire. As you'd expect at the stratospheric end of the upper luxury car segment.

Plus, a steering wheel that not only is lovely to hold but also heated, rich thick-pile carpet, climate controls for rear occupants, heated/vented seats all round, two proper foldaway tables and window blinds to block out paparazzi all make the Jaguar feel special as well as opulent, in a charming old-school way.

On the tech side, the audio system is literally a blast (Bowers & Wilkins, you know), the rather busy instruments do incorporate a GPS display Porsche Panamera-style, so your driver doesn’t have to take eyes too far off the road, while the main central screen can display images (film, TV, DVDs…) for passengers while the wally behind the wheel is left looking at something less distracting – like some boring text info on what the others are enjoying. Clever.

Also very Blade Runner is Jaguar’s now-signature rotary trannie dial that rises like a zombie from the console. On the other hand, the centrally mounted ‘3D’ style analogue clock is more rapper video bling than Replicant geeky.

Actually, looking at the instrument binnacle, it’s like Jaguar tried so hard to get the rest of the car looking futuristic and special that they ran out of ideas for the dials, and that’s a pity. Essentially a trio of computerised gauges that already look low-res and dated, they’re just not beautiful enough for this British-built icon.

Plus, said dials suffer for being too busy, though the ‘torchlight’ speed and rev-counter gradient is a cool idea. And why is there no auxiliary digital speedo readout?

While we’re complaining, the touch-screen isn’t as fast as it should be and requires a determined – and at times repeated – jab for some of the features to function.

Worse still, a couple of electrical maladies struck in our week with the XJ L. There was a phantom seat movement menace, and 15 minutes of absolutely no life in any of the systems including ignition. That was more like the bad old days of Lucas, Prince of Darkness, than a Japan-anime vision of detail perfection and utter inscrutability.

We were expecting a deeper boot too, Jaguar – although the XJ's lusciously lined unit still offers a useable 520 litres.

So the XJ L’s exterior looks like a Russian yachting oligarch ordered it, the cabin reeks of luxury and there is sufficient lounging room for four pampered occupants.

But the driver gets to have the last laugh.

As suggested by the menacing styling, 375kW/625Nm supercharged 5.0-litre V8, relatively lithe 1915kg kerb weight and Supersport name, the XJ L is no shrinking violet in regular Drive mode – fast barely describes it.

Yet pressing the Dynamic button, just by the gear selector, creates a burgeoning nuclear mushroom-cloud fury, complete with shockwave acceleration from standstill to, well, what feels like infinity… and beyond.

There’s no other way to describe how dramatically instantaneously your speed accumulates – and keeps on doing so – if you’re determined or nuts enough to try.

The tacho glows a demonic red – with the redline migrating 300rpm north to 6800rpm – while the remapped slushbox snaps through each of the six forward speeds to help contain the explosive performance.

So it’s a tribute to Jaguar’s engineers that the Supersport’s chassis doesn’t fall into a heap each and every time. Yes there is a quake effect from behind, and in the wet even superglue won’t quell the inevitable sideways two-step.

Armed with an active differential control that can lock out torque where required on less than satisfactory surfaces, the XJ L’s stability and traction controls are sublimely subtle yet toweringly effective.

Combined with the massive grip from the 20-inch wheels and tyres, there's a 24/7 safety net to keep you from veering off into another, unplanned direction.

A very welcome upshot of Dynamic mode is an exhaust baritone to send icy cold shivers down the back of a most ardent Barry White fan. The XJ L rumbles and thunders with angry intent, like the drivetrain is searching for a lighter, smaller and far less limousine-like body in which to strut its stuff, but it croons a melodic – almost melancholy – murmur when constrained by those nasty speed limits. Like a caged panther pondering a way out.

Anyway, global oil production levels of petrol consumption might be what you’re expecting.

Actually, the Jaguar’s pretty light on the juice for what it is, averaging a more-than-acceptable 16.9L/100km. Be sensible and boring, and that can – theoretically – tumble to 12.1. But that’s like commanding the Enterprise and not trying out warp mode. At least the option is yours. Thanks again, aluminium.

There’s a virtuous circle at work here too, since the steering – never a barrage of information or feedback in any Jag of living memory – at least zigs and zags through your favourite set of turns with utter accuracy, control, and composure.

While the XJ L never actually shrinks around the driver, a very satisfying rhythm and flow is possible due to the sporty handling set-up, making this a quietly quick device through a mountain pass.

And the ride! 20-inch alloys, remember. It’s sufficiently comfy. Never would you call it soft, but the cosseting, quiet and detached Jag won’t have you gritting your teeth at the first sight of a sorely neglected stretch of tarmac.

What we have, then, is a bombastic limo-missile in a loud outfit that can really dance like Fred Astaire while gingerly rogering rogue roads as well as vast distances without loosening fillings or displacing dentures – even if it’s a little vague in conveying the steering’s ultimate feelings.

It’s so nearly all the supersized luxury sedan any plutocrat could ever pawn grandpa for. The longer we spent time with the Jaguar, the more we were willing to overlook the annoying details – you know, instrumentation, flaky touch-screen, electrical gremlins.

Maybe a software update (and an extended warranty) can cure most irritants, leaving you with a vehicle of utterly kilometre-crushing capability combined with a very compelling personality.

Yes, the price is astronomical, but then so is the pile of cash demanded for a Panamera Turbo, Merc S63 AMG, Maserati Quattroporte and any other flagship limo. You can blame the pollies (mostly) for the outmoded luxury car tax for that. And even the styling might grow on you too!

Despite its price, appearance and minor flaws, the XJ L Supersport is a true Jaguar through and through. Essence of brilliance is all over this car.