There's no avoiding the $64,000 question. Has he ever given vent to his need, as it were, during a race? We both laugh. "I know drivers who do," he says. "I couldn't do that, I just couldn't. But it's actually quite common." So there we are. There is clearly an unwritten rule among drivers that they will soak each other in champagne to conceal those embarrassing wet patches.
The real $64,000 question, of course, is whether Hill will make it to the podium this season? Last year, he confounded both his own critics and those who thought that a grand prix was beyond the Jordan team, by winning in Belgium. Can he do it again? And if so, is he in with a serious shout of winning the championship, which gets off the grid in Melbourne on Sunday? "I think we have a chance," he says, guardedly. "A slightly outside chance but a better chance than last year. I will know very early on whether the car is good enough."
We are at Brackley, near Silverstone, where the new car has been rigorously tested against simulated race conditions in the Jordan wind tunnel. It is early morning. Hill has stayed overnight at the Oxford home of the team's charismatic owner, Eddie Jordan. He looks sleek and fit and raring to go. At 38, he is the oldest Formula One driver by far, and is acutely conscious of the fact. Everyone keeps asking when he will retire to his large home in Dublin to enjoy, with his wife and four children, a fortune reputed to be well over pounds 30m. "At the moment, I still feel I have something to prove," he says.
There is no doubt that, to coin a pun, he is a driven man. One theory goes that Hill has long been motivated by the desire to restore the family fortune, which disintegrated after his father, Graham, died in a plane crash in 1975. It turned out that Graham Hill had forgotten to renew his pilot's licence and was therefore uninsured.
But Hill is rich enough now to have bought his own plane - a Lear jet, which he proudly tells me flies at .8 of the speed of sound - so clearly there is something driving him beyond the desire for material reward. Perhaps it is simply that he craves more respect from his peers. For despite his world championship in 1996, there are some in the sport who disrespectfully claim that Hill is a seriously flawed driver.
It is said, for instance, that he is poor at overtaking. Is he? "There have been occasions when I've been less than committed, which has got me into trouble," he admits. For a moment, it seems as if I am going to get a show of humility. But champions as single-minded as Hill, in sports as demanding as motor racing, don't really do humility.
"I overtook Schumacher on the first corner in Hungary, which is supposed to be almost impossible to overtake on," he adds. "I took Frentzen up the inside on the grass in my last race at Suzuka. I have been through the field from the back to the front at Estoril. I think my driving ability can equal that of anyone out there, and I have other talents. I think I am very good at working with the team and getting the best out of the car. A lot of drivers don't have that strength."
Unusually, if not uniquely in the modern era, Hill did not race in Formula One until he was well past 30. He had started racing motorbikes in 1979, a hobby he financed by working as a dispatch rider in London. When he did finally graduate to Formula One, with Williams- Renault, he won three races in his first full season. Yet he did not come of age as a driver, he feels, until the following year, 1994, when he won the Japanese Grand Prix at Suzuka. "I drove out of my skin in that race," he recalls. "For me it marked a new threshold in Formula One and I think it was similar for Hakkinen at Nurburgring last year. He drove in a way he hadn't before, better than he ever thought he could drive."
Last year, Hill watched with detached amusement as the media stoked up the rivalry between Mika Hakkinen and the man everyone wants to beat, sometimes in more ways than one, Michael Schumacher. "It always comes down to two protagonists," he says. "Michael and me, Senna and Prost, Senna and Mansell. In a sense it is very similar to boxing, with all the hype and attempts to out-psyche each other. When you have two people of equal ability, a psychological advantage can make the difference. Muhammad Ali was a great one for that. By the time he got in the ring he had often reduced his opponent to an incidental, a side-show. And I really don't see any negatives about that. In fact, I think it could go a lot further. The trouble is, there is this dual standard. Everyone wants to see a punch- up, but starts tutting when there is one. Why doesn't everyone lighten up? It's entertainment."
As he would perhaps acknowledge, Hill has himself been known to forget that he works in a branch of the entertainment industry, a charge never levelled at his flamboyant father. He is uneasy talking about his father, and understandably loathes the cod-psychology which has him trying to match the old man's record. Warily, though, he admits that it would be nice to emulate Hill Snr by winning two world championships.
"He died such a long time ago, though. It will be 25 years at the end of next year. But that's not to say that I don't think about him. And although I'm not like Glenn Hoddle, I am comforted by the feeling that he's aware of everything I've done." There are, of course, people still around in motor racing who loomed large in Hill's childhood. "I remember my dad being on the phone to Bernie Ecclestone a lot," he says. Were they friends? He searches for the right words. "I think," he says, "that any relationship with Bernie is bound to lead to some level of frustration."
If he has had a proxy father, it has been Jackie Stewart. "He has always treated me brilliantly, and I have asked him for advice a few times, though of course he runs a rival team. Jackie knows all there is to know about driving. When you listen to what he has to say, to what Fangio says, to Stirling Moss, their words are as meaningful as anyone's. And when you look back at the things they did not even that long ago, you think, Christ! Look at those aluminium chassis, ground-effect cars, with the driver sitting practically on the front axle - in an impact there was nothing there. But at the time, they thought they were driving the safest cars possible."
Hill is keenly aware of the essential contradiction in motor racing, that it is presented as a family spectacle, yet its most dramatic moments involve crashes and, sometimes, fatalities. "Imola in 1994 knocked the stuffing out of everyone," he says, referring to the deaths of Ayrton Senna and Roland Ratzenberger. "Since then, the sport has been made safer and the risk element has been reduced. But you can go too far down the road of sanitising everything. We are not human beings unless we take risks. Or put it this way, the lives of people who take no risks would be even duller if there weren't people who take risks on their behalf."
Hill has always been a risk-taker. He was just five when he was introduced to skiing, and was instantly intoxicated by the speed of it. Even now, he insists that skiing is his first sporting love, and his eight-year- old son Joshua is similarly smitten. He is also determined to master surfing, and last year in Australia spent three whole days in the surf. "I relax by doing something else intensely," he says. "The trouble is that I end up doing everything in bites." Not to mention bytes. He is presently trying to absorb information technology. "I hate Bill Gates, actually hate him," he says. "I have very little time to get up to speed with computers, so when I do, I want to be able to plug in and go. But you can't, because there is barrier upon barrier. Gates is walking into the sunset with billions, having sold us a dream that's not yet there. We're told it makes life easier. It doesn't, it makes life hell."
There rants a man who cannot abide to be defeated by a machine. And it raises the question, what will he do when he does finally hang up his racing overalls? "Motor-racing has been part of my life for as long as I can remember," he says. "I think I would like to do something else next, because it is quite a claustrophobic world, with limited opportunities. If I did stay involved, I would want control over the entire sport and everyone in it. And then I would give the public passes to get into the paddock, because the hospitality business is keeping true fans further and further away. It is the same with football. But I think we might be on the cusp of realising that money is not the answer to everything." If only it were so.