I was buying lunch, but let Sir David choose the restaurant. 'It will be quiet because, sadly, it's suffering from the recession,' he assured me. 'Ask them for my special table.'
It was a symbolic choice. L'Etoile was fashionable in the Sixties, when he rose to prominence, and has remained impervious to later trends. No steel chairs and tables, no minuscule portions and, as he had warned, not many customers.
'It used to be a favourite BBC pub,' Sir David recalled, dreamily eyeing the bleak landscape of deserted tables. 'You would come in here and find Alasdair Milne, Paul Fox, anyone who mattered.' Milne was the first victim of the Thatcherite revolution at the BBC and Sir Paul retired a couple of years ago. By contrast Sir David, 53, is still very much with us, still wearing those Sixties striped shirts, still doing much the same on screen he has always done, with the same impeccable aplomb. Just occasionally, he switches channels for variety.
He was in luck. One friend from the old days did arrive. James Clavell, the author, had just flown in from New York and came over for one of my guest's famously effusive welcomes. 'Lovely man,' Sir David confided, as the writer left us and headed towards his own table.
Why the new knight's television career continues to flourish puzzles some critics. He is a sound but not flashy interviewer, yet as soon as his Sunday morning programme threatened to become extinct along with
TV-am, which broadcast it, the BBC stepped in with an offer to accommodate him - and let him sell the satellite rights to BSkyB into the bargain.
A new series of Through the Keyhole, the peeping-Tom game show he helped to devise, starts on ITV in March. The following month, for Carlton, he begins a London-only version of his old audience-participation Frost Programme. And he has a monthly interview series in America, shown here on BSkyB.
He has the unrivalled ability to attract big- name guests, who clearly prefer to be lightly poached by him for breakfast rather than grilled to a frazzle later in the day by one of the acerbic Dimblebys. It was John Major for the first Breakfast with Frost last Sunday, John Smith will be next and Norman Lamont after that. For a change of pace, Clint Eastwood is promised around Oscar time in February.
Some say Sir David's interviews are now bloodless. Certainly they have changed since the Sixties, when his victims included the young Rupert Murdoch, who retired wounded and vowing revenge, and the fraudster Emil Savundra, who wept when Frost weighed into him. Yet Mr Major was allowed to proceed to his post-interview croissants with both his tear ducts and his dignity intact.
Why, for instance, was he not quizzed about the most embarrassing of all his government's foul-ups, the attempted pit closures?
'That would have been next on my agenda if there had been time. There were three major crises and I dealt with the two I thought most fruitful - the exchange rate mechanism, then the Maastricht debate and Lady Thatcher.'
But why nothing about the future of the Chancellor of the Exchequer? 'He'd been asked at length about Lamont by Jim Naughtie on The World at One on Thursday.'
Despite these gaps, Mr Major was persuaded to say things about the ERM, Lady Thatcher and the Royal Family that made headlines next day. Sir David was satisfied.
'A question can only be judged in the end by the answer it provokes, not what it does
for the ego of the interviewer. You have to avoid the knee-jerk option of being full of sound and fury. It's no good unless it signifies something.
'There is a form of huffing and puffing and adversary questioning that leads nowhere. If I asked you: 'Don't you agree, Mr Leapman, that your entire life has been totally wasted?' that's too easy. You would be able to say: 'No, I rather like it,' and that would be the end of that.
'But what if I ask you: 'Which of your many articles do you most regret?' You can ask just as intellectually testing questions in a civilised way as in a rumbustious way. Think back to my question to Neil Kinnock before the 1987 election, when I asked if Britain became unilateral would he send troops to fight an enemy armed with short-range nuclear weapons. It was a very difficult question under any circumstances.'
Part of the reason why you do not have to be so rude to politicians today as in the Sixties is, he believes, the pioneering work he and his colleagues did on That Was The Week That Was.
'It triggered off a very healthy irreverence. To assume that everybody in politics was there for noble self-sacrifice was absurd. Their motives were as self-serving as anyone else's.
'But when you trigger a swing of the pendulum it can go too far in the other direction, and politicians are thought to have worse motives than other people. That's equally inaccurate. Because they have power they aren't necessarily venal.'
Sir David modestly refrained from mentioning his knighthood in Sunday's programme, but is delighted at the reaction to the honour.
'I was knocked out by the letters from viewers. One wrote from Halesowen: 'Now the impossible will happen and we'll have a knight in the morning.' ' For a celebrated wit, he is inexplicably fond of really terrible jokes.
He was overwhelmed, too, by the press reaction, although anyone without his Panglossian ability to look on the bright side might have found it a bit snide. He acknowledged with sorrow the unambiguous disdain of the Independent on Sunday's television reviewer ('How do you send up a country which has just knighted David Frost for services to himself?') but saw only goodwill in the comments of his old comrades in satire, Richard Ingrams and Christopher Booker, which, though affectionate, could also be read as slyly patronising. He was even flattered by a distinctly double-edged cartoon in the Sun.
He has had failures but they do not rankle and he does not dwell on them. The two television companies he helped to form - London Weekend and TV-am - both began with hopelessly unrealistic programme ambitions and both hit trouble soon after they were launched, although, alone of TV- am's Famous Five founders, he remains on the board of the now disenfranchised company. ('The Famous One,' he quips.)
Not all of his books have been successful and one of his most exotic failures, a bid to open a chain of Japanese steak houses, collapsed when it was calculated that he would need to fill every table six times a day to make it pay. Now the episode crops up as a problem on test papers for students at Harvard Business School.
He spreads his talents a bit less thinly nowadays, partly because he likes to spend time with his wife and three sons aged eight, seven and five.
'I can't exactly trace what I give up to spend the time I do with the family. Before I was married, if I was involved in six projects and fully stretched, and a seventh irresistible one came along, I'd say yes to that and fit it in. Now I'm as busy as ever, busier in some ways, but I don't in general schedule meetings for 6.30 in the evening or go to cocktail parties.'
A man who has been at the sharp end of the media for 30 years must have enemies, but Sir David does not acknowledge them. American mothers scold their children: 'If you can't say anything nice, don't say anything,' and I suspect he may have been subject to the same admonition as a boy, for when anybody's name cropped up in our conversation it was always greeted with a Frostian paean of praise and affection.
Michael Palin? 'A lovely, enchanting and good man.' Jeremy Paxman? 'I admire him.' Norman Tebbit? 'A very genial man' (some mistake, surely). Billy Graham? 'Great respect for him.' Michael Shea, the Queen's former press officer? 'A lovely man, I really like him.'
Lunch consumed, the chablis drunk, he summoned the cigar cabinet and sucked on a satisfyingly huge Havana. James Clavell left just before we did.
'Bless you,' Sir David cried after him. 'Good luck with the new book. Looking forward to it.'
The closing credits, the familiar theme music welling gradually to full volume were, I later realised, all in my imagination.
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