Let’s give BMW credit where it’s due: the X5 has proved something of a knee in the goolies for critics of crossover. But then it would have been hard to predict, back in 1999, that what was being touted as the world’s first Sports Activity Vehicle would become such a spectacular global hit. Nearly 600,000 X5s have been sold to date, almost half in the US. Demand rose sharply as soon as people clapped eyes on the genre-bending all-rounder and hasn’t dipped significantly since.

With rivals from Audi, Range Rover, Mercedes, VW and Porsche turning up the heat, the decline was probably due to kick in any moment now, which makes the timing of the new X5 (bigger, better, smarter) just about perfect.

Setting aside, for a moment, the question of whether anyone actually needs a vehicle like an X5 over, say, a 5-series Touring, one of the reasons the original design sold so well – apart from the badge – was the fact it didn’t handle like a shed on the road (no-one cared what it handled like off-road) and had a decent range of engines to exploit the dynamic talent. Core Bee Em traits. Until the Cayenne came along, there wasn’t a sportier SUV (or SAV). And if you removed straight-line grunt from the equation, the BMW probably still just had it.

Although the new X5 doesn’t look dramatically different to its predecessor, BMW’s efforts to re-open the gap between it and the competition have been prodigious and, rather refreshingly, don’t involve inserting the largest available engine under the bonnet. The £49,945 4.8i SE we’re driving here at the international launch in Greece is by no means backwards when it comes to moving forwards (150mph, 0-62mph in 6.5sec) but its 355bhp looks almost modest alongside the 500bhp-plus outputs of its more deranged rivals from Porsche and Mercedes.

The new bodyshell (think pumped X3 with better proportioning and detailing) is much stiffer than before but no heavier. And a lot of work has gone into getting the engine and gearbox as low and as far back in the car as possible, dropping the centre of gravity with the aim of increasing agility and grip.

Then there’s the new double-wishbone front suspension, the usual gang of electronic stability and traction aids, fourth-generation run-flat tyres, BMW’s sophisticated on-road-biased xDrive four-wheel-drive system and the options of BMW’s Adaptive Drive, which combines electronic damping control and hydraulic anti-roll bars to optimise body control in fast cornering, and Active Steering, which varies the steering ratio according to speed. The new six-speed automatic gearbox is claimed to cut shift times by 50 per cent over the old model and is operated via a new SMG-style shift lever.

It doesn’t look it from the outside but the new X5 is significantly bigger than the old car, being some 190mm longer and 60mm wider. The extra length provides more rear legroom and the space for an optional third row of seats, though they’re only really suitable for children and the boot shrinks to a meagre 200 litres with them in place. BMW thinks most buyers will opt for the standard five seats and 620-litre boot.

As with the external styling, the cabin design carries through the ‘grown-up X3’ theme, further distancing the X5 from the 5-series saloon, though, arguably, it’s none the worse for that.

But it’s on the move that all BMW’s hard work shines through. The new X5 feels lighter, lither and handier than its predecessor, delivering the kind of steering precision, body control and grip that many an executive saloon would be hard-pushed to better while, at the same time, ramping up comfort and refinement to levels much of the opposition simply can’t live with, even on the run-flats.

Performance from the big petrol V8 is strong rather than startling, but the six-speed auto is keen – often too keen – to keep things on the boil, kicking down at what sometimes seems absurdly high engine speeds and with little of the predictive finesse displayed, for instance, by the auto ’box in Jaguar’s new XKR.

Overall, though, the new X5 moves the game on as BMW intended. It may have lost a little aesthetic character, but the gains are certain to keep the customers rolling in.