'You must be joking,' I retorted - rather rudely, since the conversation was at Sir David's summer party - when he explained there was no fee and that I would have to travel from Scotland on Saturday evening to be sure of getting on the programme at the crack of dawn on Sunday.
'I am sure,' I said rather grandly, 'there are lots of MPs who will respond happily, but I'm not one of them.' (I had in mind the old story from Tonight days of the producer who told a senior but obscure MP: 'Our fee will be pounds 25,' to which he responded: 'I'll bring my cheque with me.')
My attitude only seemed to whet his appetite because we eventually agreed that I would appear down the line from Edinburgh this week. I was not only without breakfast (there being only the one ever-helpful engineer on duty at the Edinburgh studios), I was without Frost. He was on holiday and Martyn Lewis was standing in.
Now David Frost belongs to that select band of interviewers with whom MPs long to appear for the sake of their egos. I have lost count of the number of times over the years that he has 'done' me, so I regarded Martyn Lewis as no disappointing substitute.
Mr Lewis belongs to the self-advertised good news school, and I don't think I've ever known him to ask an aggressively hostile question. Indeed, he is such a decent chap that some years ago in Simpson's of Piccadilly, when he momentarily mistook me for the pyjama salesman, he was so embarrassed that he invited me to lunch.
Yet Frost and Lewis have one thing in common with the blessed Jimmy Young of Radio 2: they behave so congenially with the interviewee that the guard drops and unintended truths slip out to turn into their own news stories.
This is the very opposite of the similarly effective technique of Brian Walden, whose method of creating news stories was to improve on the answers he had been given. 'Now let me get this absolutely clear, Mr Steel, what you are telling me is that there are certain circumstances in which you would murder David Owen.'
Actually, I am being slightly unfair. I recall one election when Walden had come to Glasgow for the ritual hour-long live interview with me as party leader, and he began the programme while my helicopter was descending, late, on the studios. I rushed in after his introduction during the news headlines. The viewers would have found nothing untoward and a robust exchange followed with no prior conversation.
It is a mistake, though, for politicians to choose their interviewers. Margaret Thatcher adored Walden and he was somewhat besotted by her, with the result that nothing of value emerged from their encounters, unlike most of his probing interviews. Her most revealing faux pas occurred with David Dimbleby, whom she obviously despised, and with Kirsty Wark of BBC Scotland (soon to be with Newsnight), who did not have to put up with the patronising feminine wiles the then-prime minister regularly deployed on her male inquisitors.
If it is true that John Major refused to be interviewed by Jeremy Paxman because he is abrupt and disrespectful, that is an error of judgement. The only thing to do is to treat interviewers as robustly as they treat you. Get your attack in first. A few weeks ago, I was forced to appear on Newsnight in a dinner jacket, having raced straight from an ambassador's dinner with 30 seconds to spare.
'What on earth are you dressed like that for?' hissed Paxman cheerfully under the opening music. 'I am just trying to lend some tone to your programme,' was my response. The discussion thereafter was impeccably civilised.
Sir Robin Day had a wholly unjustified reputation for being rude. It was something to do with what the late Frankie Howerd called 'those croo-ell glasses'. In fact, Sir Robin is always courteous, but because he is amazingly well-prepared, he suffers neither fools nor evasions gladly, and is tenacious in pursuing his quarry.
The most difficult interviewers for the ordinary mortal politician are those who are experts in their field. John Cole, for example, usually knew more than his victims about what was going on that day, and could be devastatingly awkward. My own worst moment came on an extended News at Ten interview with Sir Alastair Burnet, former editor of the Economist, on some arcane economic issue that I had not anticipated, and which left me waffling helplessly for what felt like a quarter of an hour.
The most difficult interviews are those conducted by regional TV pundits, or worse, local radio ones: household names in their own patch, who want to make their reputation by flooring the visiting VIP with a surprise question on a local issue. Wriggling, evasion and waffle reign supreme on these occasions.
Politicians should be chary of straying into the non-political interview. I suppose I did two or three Wogans. The interviewee sat almost with his back to the studio audience while Terry faced them. You were merely a bit part of the great man's show, not the subject of it.
Early clips of historic radio interviews, regularly repeated, show interviewers to have been obsequious and little more than feed men to the great. I trust that what is now being proposed by the BBC governors is not a return to such rituals.
The truth is that the TV interview, properly mounted, is a much more demanding and testing event than a speech at a public meeting, or question time in the House of Commons. The viewer can spot the failure to answer and there is no escape in circumlocution.
Dictators around the world address their people uninterrupted. The face-to-camera message certainly has its place, but in a mature democracy, the probing interviewer is a principal means of reasserting public accountability.
Sir David Steel is the Liberal Democrat MP for Tweeddale, Ettrick and Lauderdale, and a former leader of the Liberal Party.