Lots of people have bought S-Types. Over 135,000 of them worldwide to date. Yet there is a feeling amongst those whose sensibilities run deeper than a taste for wood, leather and cod-Britishness that the S-Type isn't as real a Jaguar as it ought to be.

I once put it to product development director Nick Barter that the S-Type was American Ford's view of what a Jaguar should be. His denial was vehement, but I sensed a nerve was touched. After all, the S-Type had to share much of its underskin architecture with a Lincoln LS, and in seeking to appeal to a wider market the interior design lost out on recognisable Jaguarness. The style could have come from anywhere.

Not so the outside. It's now well known that the S-Type shape is the front of one styling model, the middle of another and the tail of a third. But Jaguar's research showed that in seeking to update the S, the style should stay the same, so some people must like it. And outside, at least, the design features are clearly Jaguar.

Now, look at the 4.2 V8 pictured here (bigger engine, more power, major-but-subtle 2002 MY makeover). Looks better, doesn't it? Two tiny changes have done the job. The side windows are fully encircled in brightwork, and the front grille looks more Jaguar Mk2-ish with the badge incorporated at the top. It gives the face a new focus.

Inside, mid-Atlanticism is out and a proper Jaguar dash is in. The theme is strongly XJ/X-type, and those horrid, dated-looking LEDs have gone in the bin. So has the elbow-bashing handbrake lever, because the park brake is now electric. If the transmission is automatic (as it is in all V8 S-Types, now a six-speed ZF unit) then the parking brake is too. It engages when the key is removed and releases when the selector moves out of park. Another piece of cleverness, optional this time, is the electrically-adjustable pedal box.

Short-legged drivers no longer need to sit too close to the steering wheel. You can also have a sat-nav with destination set by postcode.

So much for the parts you can see. The parts you can't, however, are what make most of a car's driving feel. And they've changed quite a lot. The rear subframe is now rigidly mounted, and the rear roll centre is raised. Both ends have new suspension arms, aluminium at the front and mounted on a new subframe, and the optional CATS adaptive-damper suspension and ten per cent stiffer bodyshell further sharpen the responses. Springs, dampers, bushes and anti-roll bars are all recalibrated, and a DSC system which tames understeer as well as oversteer is standard on all versions. Those Lincoln-clone suspension parts are just a memory now.

Engine changes are simpler; just a longer stroke for the V8, to give exactly 200 more cc and a power rise from 276bhp to a round 300. The V6s get fully-variable inlet cam timing like that of the V8s, and there's now an entry-level 2.5 V6 beneath the existing 3-litre. But it's the V8 we're interested in here. And even in soft-touch SE mode (there's also a Sport version) it's a truly transformed S-Type.

Unless you've driven the S-Type R, you would think the 4.2 V8 is surely engine enough. It emits a cultured V8 beat, rising to a distant cackle as the pace piles on, which you don't hear in the R because the supercharger whine smothers it. It's torquey and revvy in equal measure, and squirts to 60mph in just over six seconds even though an S-type SE hardly looks to be that sort of rocketship.

The six-speed autobox allows the engine to work in its best range, and the small steps between ratios help keep shifts smooth. And, typical of the best modern autoboxes, the revs blip up for a smooth downshift just as the lower ratio slips into place. You can intervene manually with the J-gate, but there's little point when the box almost always does the right thing all by itself.

Then there's the matter of bends and bumps. After the R version this S-Type's steering feels a little lightweight, but you soon calibrate your senses and discover that consistent, believable responses and confidence-inspiring accuracy lurk within the ZF rack with its uniquely Jag valving.

It's a big and hefty car, but that is not how the V8 SE feels even on its relatively soft suspension. The forces acting within it all seem to be channelled in the right direction, making for an unflustered and deeply satisfying drive which somehow engages you even more than, say, a new E-class does. At last, the S-Type is the car it always should have been. I couldn't live with that cheesy half-wood steering wheel, though.