If anyone, back in 1977, had predicted there would come a day when people would look at that year’s Frost/Nixon television interviews as an event so rich in drama, it would generate a critically acclaimed play and a film, we would have thought them insane.

The critical consensus among the chattering classes was that the event was all a bit of a bore. Like millions in Britain, the journalist Christopher Booker watched the interviews and was shocked by the “sheer stumbling, incoherent, sentimental, embarrassing amateurishness of it all”. The television critic of The Times summed up the widespread sense of disappointment by declaring: “It was clear that David Frost let Mr Nixon escape in the interrogation.”

So, should we thank the dramatist Peter Morgan (The Queen, The Deal), who wrote the original play on which the director Ron Howard’s film is based, for showing us the dramatic gold so many of us erroneously dismissed as media dross? Or have Morgan and Howard fooled us by presenting this overhyped, shallow media event as some great battle for truth between two great forces of modern democracy: media and politics? Answer: yes, we’ve been conned. Frost/Nixon is a historical fraud, a mind-boggling travesty of the truth. Let me hasten to add, however, that it is without doubt the most gripping, entertaining, dramatically clever and fascinating fraud I’ve ever seen.

I don’t, of course, mean that it’s a fraud because it takes liberties with a few facts.

It does that. Events are compressed and scenes invented, like the late-night phone call that Frost (Michael Sheen) gets from a drunken Nixon (Frank Langella). And the film doesn’t make clear that Frost, along with his mother, had been a guest at Nixon’s White House, or that Nixon got 20% of the profits for media sales from the interview. Never mind all that.

No, what bothers me is the way the film leaves you with the impression that good old Frostie got the confession out of Nixon that the world wanted to see. He didn’t. He was more patsy than Paxo. In the actual interview, Nixon’s so-called admission of guilt has more caveats, more ambiguities and circumlocutions, than a WMD intelligence report. Nixon explicitly said to Frost: “You’re wanting me to say that I participated in an illegal cover-up. No.” At the climax of Howard’s film, however, Frost finally lands the knockout punch and gets a confession of wrongdoing.

As the film makes clear, Frost understood the psychological need of the American people for a confession. Nixon had left office in disgrace, but had never been put on trial or given an interview on Watergate. (It’s no wonder that people watching him on television mistook a few crumbs of contrition for a true confession.) So, once you realise that what you see on the screen has very little to do with historical truth, you can sit back and enjoy what is a great work of media mythmaking. It tells a fascinating story of two men who want to get back their place in history via television.

To do this, Morgan turns a political interview into an Ali-Foreman boxing match. It’s the rumble in the living room, with Frost portrayed as the underdog, a lightweight chat-show host facing the political heavyweight. “Only one of us can win,” Nixon says. The stakes are high, and the film slowly builds them higher and higher, so that the media hustler Frost becomes our hero. If he fails to deliver a knockout blow, Nixon rehabilitates his reputation; if Frost wins, Nixon will go down in history as a crook. Once the terms of the interview are agreed, both men, and their research teams, go into preparation.

At the first interview, Frost comes out slugging and misses with the question: why didn’t you simply burn the tape? Nixon swats that one away easily enough. In subsequent interviews, Frost is unable to nail Nixon over Vietnam and Cambodia, and it looks as if it’s all over for David in his struggle against Goliath. The turning point comes when, one night, three days before the final interview, a rambling Nixon phones him and talks about how they are both men from humble backgrounds who have suffered at the hands of snobs. Morgan has cleverly used a perception of Frost that still resonates. Frost was looked down on by his peers — Jonathan Miller, Peter Cook — not because of his class, but for what they saw as his lack of real talent. After this late-night conversation, Rocky . . . sorry, Frostie starts to get down to some serious training. The final interview is a brilliant, tense encounter, even though the original was amicable and rather dull.

Both Sheen and Langella look nothing like their subjects, yet both manage to make these men more interesting and sympathetic than you would ever imagine. Langella wisely avoids trying to imitate Nixon, and gives an outstanding and convincing performance. He has freed Nixon from the association of sleaze and turned him into something tragically Shakespearian. Frost is shown as a man with no principles, no political convictions, no desire but to make money and be famous again in America — yet Sheen makes him human and likeable. Never mind Nixon, it’s this rehabilitation of Frost that bothers me. Here is a man who has spent nearly 50 years sucking up to the rich, the famous and the powerful, and now, thanks to this film, he will go down in history as the great inquisitor who got the truth out of Richard Nixon. Rarely has bad history become the basis of such a great film.

15, 122 mins

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010