More importantly, he is still held in enormous affection by viewers. What else could explain the sale of 25,000 copies of his memoirs, As It Seemed to Me? The book has remained in the Sunday Times Top 10 Bestsellers List since it was published at the beginning of April. On promotional tours around the country, Cole has been mobbed as if he were the lead singer of Take That - albeit in a funny coat. It's enough to make you think that politics is the new rock'n'roll. Robin Oakley - his successor as the BBC's Political Editor - had an impossible act to follow. So just why is Cole still famous enough to be regularly accosted by what he calls "the green ink brigade" on the Tube? Why is he esteemed so long after he has stopped receiving the oxygen of publicity generated by almost daily television appearances?
Wilson puts it down to a rather outdated concept in both journalism and politics: "I don't want to sound too much like a form teacher, but he's transparently honest, that shines through. He's a very moral man, upright in a rather old-fashioned way. Maybe that comes from his branch of Protestantism, Presbyterianism. He isn't a table-banging Paisleyite, he's much more like Cromwell - 'I beseech you, in the bowels of Christ, think it possible you may be mistaken.' He's striving to do the right thing - a 17th-century Protestant ideal."
In political interviews, Cole certainly played it straight, neither adopting the bully-boy tactics of a Paxman nor bowing and scraping a la David Frost. In one memorable exchange in the film, Cole takes issue with Geoffrey Howe over unemployment. "I was riveted," Wilson remembers. "There was John telling a former Foreign Secretary and Chancellor, 'It's just not good enough'. Geoffrey was perfectly happy afterwards because he knew where John was coming from. He wasn't just there to ambush Geoffrey. Politicians trust John. He never reveals his sources. They talk to him because he would never say where the bodies are buried."
Cole's outmoded sense of fair play even extends to the virtually unthinkable: he believes most politicians are fundamentally decent. Forrest Gump's doctor catches the prevailing mood when he says at the beginning of that film that Gump's back is "as crooked as a politician".
"I don't share the view that all politicians are crooks, as bad as estate agents, or even journalists," Cole muses down the line between book-signings and Harold Wilson obituaries last week."Most politicians come in with a sense of idealism. They make inevitable compromises - the party system imposes compromise - but most of them retain a reasonable amount of their original intention to do good. Frankly, compared to other jobs, the money and the working conditions of an MP are not such as to be terribly attractive, so I must assume they have a sense of public purpose.
"I do also find them amusing company," he continues in this unfashionable vein. "I'd prefer to be reporting the doings of politicians rather than those of City men or businessmen. Some of them are wise, too - and I don't widely use the word wisdom. Harold Wilson made many mistakes, but when you were just sitting and chatting to him about ordinary things, you were always getting sound advice. You wouldn't necessarily say that of everybody you met on the Tube. That's the reason for my love affair with the species."
Not that he's lived happily ever after with every politician. "Broadcasting is all on the record, and that's where awkwardness can come in," Cole explains. "You're asking politicans to do things they may not think are to their advantage. Gerald Kaufmann, for instance, makes his own rules about broadcasting. He doesn't like entrusting himself to soundbite-ism, to the fact that I choose 45 seconds from a 10-minute interview with him. The more suspicious want to set the agenda. Gerald can be awkward in that respect."
Mrs Thatcher could be awkward too - no surprises there - but Cole did once succeed in catching her off-guard. "The difficulty about interviewing her," he reflects, "was that she was the supreme professional. You had to work hard to get news out of her. I was once walking over to No 10 with Glyn Mathias from ITN, and he said, 'What questions are you going to ask her?' I said, 'If you ask her about the weather and I ask her about her horoscope, we'll both get the same answer: Government economic policies are working.' You had to surprise her, get under her guard. When I interviewed her after she'd announced the 1987 election, she was burying me in statistics when I saw a chink for an old man to ask a woman no longer in the first flush of youth whether this would be her last election. She replied, 'Oh no, I intend to go on and on and on.' This was not such welcome news to some of the electorate, nor to some of her younger colleagues. Kenneth Baker said in his memoirs that she regretted it."
Those are the sort of moments for which Cole will be remembered. For an apparently untelegenic older man - he's now 67 - with a wiry hairdo and bottle-bottom glasses, he had tremendous presence. His appearance with a microphone outside No 10 always guaranteed compelling viewing. This was allied to a cogency not always manifest in political reporters. In his own phrase, Cole aimed to provide "politics for grown-ups". Cole was also immune to Westminster Fever. "When things got paranoiac during Mrs Thatcher's time," Wilson says, "John always kept his feet on the ground. That's why he kept ahead of the pack in Thatcher's leadership crisis - journalistically his finest hour - because he was rooted in real politics."
We could not, of course, close this bulletin without mentioning Cole's accent, the harsh Ulster brogue so incessantly sent up by Spitting Image, Private Eye's "Hondootedly" column and countless budding impressionists. As with everything, Cole is sanguine about being a figure of fun."I don't object - that would be too strong - but I do find it ludicrous that when we're nearly in the 21st century, people around this diverse country of ours are still surprised to hear a Scots, Geordie or Irish accent rather than Received Pronunciation English."
Even on the subject of his mockers, though, Cole manages to deliver a rallying-cry for a Cromwellian sense of decency. "The Spitting Image puppets are good, and the impressions are OK, but they haven't a political thought in their heads. I don't think those guys believe in anything. It's the same with Private Eye. If you believed Private Eye's politics, you'd be looking for a guy on a white charger to ride in and rescue you. We already had him. He was called Mussolini."
'A Progress through Politics', Sun 9.10pm BBC2