Instead, Williams went with his wife to the BBC TV studios in London and watched the live broadcast in the early hours of the morning. Mansell, six points ahead, was the overwhelming favourite, just as he is at Silverstone for today's British Grand Prix.
What happened that day has become one of the most enduring images in sport. Needing to finish only third to become champion, Mansell was cruising in that place when a rear tyre exploded. Prost, meantime, took both race and title. 'I'm very sorry for Nigel,' the Frenchman said afterwards. 'He deserved to be champion this year. But probably I'm more sad for Frank . . . '
Earlier that year, Williams had been grievously injured in a road accident in southern France. His team had been testing at the Paul Ricard circuit, and afterwards he was driving back to Nice for an evening flight. In the accident he broke his spine, since when he has been paralysed from the shoulders down.
The goodwill behind Williams was almost tangible. Prost found himself unwittingly playing the sort of role Nat Lofthouse had when his two goals for Bolton Wanderers in the 1958 FA Cup final put paid to the rest of the nation's hopes of a victory for Manchester United only three months after the Munich air disaster. Whether or not you were a fan of Mansell or Piquet, you wanted only good things for their boss. There has always been huge affection, as well as respect, for Frank Williams.
'I'm a realist,' Williams is fond of saying, and he said it then. 'Everyone was saying Nigel had to be world champion, with his points advantage, but I thought that was a load of old rubbish. I'd been in racing too long to believe it. I don't take anything for granted. In situations like that, I always think it's more likely something will go wrong.'
Cataclysmic for anyone, there seemed an extra dimension of cruelty in Williams's sudden incapacitation, for the man had previously exuded vigour, and routinely ran 10 miles a day. By nature an obsessive in all things which capture him, he loved to run.
Two weeks after Williams's accident came the first race of the season, in Brazil. Before the start, all the drivers and team owners held up a banner for the television cameras: 'Don't worry, Frank. We're minding the shop.' Williams, in the London Hospital, saw none of this at the time, but later in the day Piquet - in a Williams - won the race, and that he was able to take in.
For some time his life hung in the balance, but he came through succeeding crises, and by July was well enough to attend the British Grand Prix. By the end of the year he was back to work occasionally, and it wasn't long before this was seven days a week. Just as before.
Not for a second, he says, has he ever felt sorry for himself, and if this borders on the incredible, it is not so when you know the man. 'The accident was entirely my fault,' he has always maintained. 'I can blame no one else, and, in fact, I regard myself as extraordinarily lucky. After I hurt myself, I had a wonderful wife and family to take care of me, and a job to come back to - more than that, a job which is a passion. In this situation, you know, a lot of people can't work afterwards, and that's awful, not least because then you have the time to feel sorry for yourself. That's why I'm so fortunate. The biggest adjustment I've had to make is that everything takes so long now. I've always been impatient, I suppose.'
As Williams says, his job is his passion. There is no man who loves motor racing more. 'When I was in hospital, I began to think about other things, taking holidays, listening to music more, and so on, but as soon as I was back at work, I was back to normal. All I could think of was winning the championship again.'
The pit lane at a grand prix circuit makes for a hostile environment. It is noisy, bustling, somehow violent, and there is never enough room. Yet this is where Williams is always to be found, sitting in his wheel-chair, communicating by means of the head-sets which are standard issue in Formula One. He never misses a race; would not dream of it.
During his year away, Williams Grand Prix Engineering Limited was in strong hands, notably those of Patrick Head, not only the team's chief engineer, but also its bedrock. Their partnership, begun in 1977, endures to this day.
Now 50, Williams was born in South Shields. His parents parted when he was young, and he acknowledges he was never close to either. Friends suggest this is perhaps the source of his resolute emotional toughness. From his earliest days, though, he can recall a passion for cars, and in his teens this focused on racing. 'It's everything to me. I've never touched booze, never smoked, but racing really is like a drug to me. And I'm completely hooked.'
At first he had aspirations as a driver, but there was not the cash to go with them. Nor, he soon acknowledged, the talent. But if he had limitations as a driver, already there were the glimmers of a world-class wheeler-dealer. He went into the business of buying and selling racing cars, and by 1969 had progressed to the point of starting up his own Formula One team.
You could do that then; there was no obligation actually to build your own cars in order to enter for the world championship. Williams bought a Brabham, some off-the-shelf Cosworth engines, and installed in the cockpit Piers Courage, son of the brewery family, Old Etonian, and perhaps the closest friend of Williams's life.
'I'd come from a poor background, and had none of his privileges or self-confidence at that time. But in racing his background rather worked against him: how could someone with so much charm be tough enough? You tend to be suspicious of racing drivers who are good blokes] And Piers never had access to family money for racing - he was as broke as I was.'
Nevertheless, the shoestring outfit did remarkably well in that first season, taking two second places, one of them at Monte Carlo. But in 1970 the debonair Courage was killed in the Dutch Grand Prix, and perhaps Williams's attitude to racing shifted for ever.
'Life,' he remembers, 'got very tough the next day. But I can't say that I considered getting out of the business. Not for a second. But after Piers died, it was a matter of going racing for different reasons. I was devastated. Even now, when I hear Beethoven's Sixth, I think of him immediately, because that was his favourite piece of music. Looking back, we buried a lot of drivers in the Seventies, didn't we?'
Somehow the team stayed in business, Williams by necessity acquiring something of a reputation for paying last year's bills with this year's sponsorship. It was not until the late Seventies that he made the breakthrough, acquiring the services of Patrick Head, then substantial backing from Saudi Arabia, then the driving skills of the Australian Alan Jones.
In 1979, Jones won more races than anyone else, and the following year the title was his. After years of mere survival, Williams were suddenly the yardstick of Formula One.
Since then, there have been many great years, and both the Finnish driver Keke Rosberg and the Brazilian Nelson Piquet have become world champions competing under the Williams banner.
Ironically, the team's most successful driver - in terms of victories - has yet to win the title, but Nigel Mansell, after his remarkable run of six wins in eight grands prix before today's, looks set to do it at last this season. He and the highly sophisticated Williams-Renault have been essentially untouchable throughout 1992.
Williams gives the impression that he perhaps admires drivers more than he likes them. 'The best drivers are not where they are because they're nice guys,' he grins cynically, but not without affection. 'For the most part, they're bastards, quite honestly.' The era of Courage, of the 'gentleman racer', is long gone. Perhaps there is simply too much at stake now.
As Williams says, though, he is 'a realist'. As the game changes, change with it, or get out. Where once grand prix racing was merely Williams against McLaren, now it is also a matter of Renault taking on Honda, Camel versus Marlboro, and like that. Big business, big money, big expectations.
What doesn't change is Williams's fundamental love of what he does. 'One thing I learned when we started to be successful is that when you get used to winning, you absolutely hate losing. Yes, it's undeniable that racing has changed out of sight, and not just in a technological sense. For the most part, it's just commerce now. But between two and four on a Sunday afternoon, it's still a sport, and always will be. I simply can't imagine life without it.'
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