To London’s glamorous Leicester Square, then, and the opening night of this year’s London Film Festival. Sitting inside the Odeon cinema, watching a live feed of the red carpet activity outside, a brief if slightly disorientating Hall of Mirrors moment unfolds on the big screen. Frank Langhella, who plays the former American President in Frost/Nixon, is being interviewed on screen, while, about two feet away from him, the real David Frost is working the crowd.

It’s a weird moment of real life and fiction gently brushing past each other. And, in much the same slightly meta way, I’m reminded that Frost/Nixon itself is a film adapted from a stage play based around a series of TV interviews that were, themselves, the residual effects of some taped phone conversations. Meanwhile, the actor cast as David Frost, Michael Sheen, is probably best known for playing Tony Blair; another shrewd media operator and charismatic opportunist. It perhaps says much about Frost’s shark-like ambition, and his vain obsession with the whirl of celebrity, that, for much of Ron Howard’s film, I found myself rooting for Nixon – that’s right, the disgraced former American President, the one who authorised war in Cambodia causing countless civilian deaths, and who lied about Watergate. Him.

It’s to playwright Peter Morgan’s credit that he can elicit this response from his audience; hey, it’s Frost we should be backing, right? But it’s hard to like someone with such a gimlet-eyed lust for success; as his one-time producer Ned Sherrin told Time Magazine in 1977, the same year as the Nixon interviews, “David would quite like to be Prime Minister. And the Queen. And the Archbishop of Canterbury. But being only one would limit him a bit.” Certainly, you see the way he flinches when people refer to him as a “talk show host” – his ambition reaches far higher than that. Which is why, after hearing the viewing figures for the President’s resignation speech, he wants to interview Nixon. This’ll be his making in America, surely? Dragging producer John Birt (yes, him) off to America to sign up Nixon then pitch the idea round the networks, you become potently aware that there’s no actual plan here. Entrepreneurial courage, or stunningly hare-brained scam, executed with no forethought, that could well be Frost’s undoing..? It’s impossible to cheer him on, underdog style, because there’s so little that’s actually likeable about him. He has charm, sure – but it’s the sociopathic charm of someone who’s going to calculate your value in a nanosecond and act accordingly. He seems to have an almost non-existent connection with people around him. His relationship with Birt is professional; he chats up Caroline Cushing on a plane and they become lovers in the film, but there’s no evidence of a sexual dynamic between them. He has so many premiers and parties to attend, he barely has time to muck in with Bob Zelnick and James Reston Jnr, the two researchers he and Birt employ to help fill out Nixon’s backstory. Sheen plays Frost pretty much as he did Blair in both The Deal and The Queen; that is to say, as something of a tosser. And he does it brilliantly.

It says much, perhaps, about how an audience perceives a villain that we frequently find them more interesting characters than heroes. So it is with Richard Nixon, American politics’ own Dark Lord of the Sith. But, weirdly, he comes over as far more likeable than you might otherwise imagine. There’s plenty of surprising evidence of a dry wit and a mercury-fast intelligence; in conversation with his devoted aide Jack Brennan, he suggests taping Frost’s phone. “I know a couple of Cuban guys with CIA training,” he deadpans, then a beat while Brennan’s jaw hits the floor and then: “I’m joking…” Then there’s the physicality; Nixon’s wounded bear gait, that low, chewy drawl, a certain joviality under which seems to lurk a vague, un-defined sense of menace. It is, of course, a fantastic part, and one Frank Langhella handles admirably, perhaps following Anthony Hopkins’ lead in Oliver Stone’s biopic by playing rather than mimicking the man. There is a sense of exaggerating, too, the publicly familiar traits of Nixon – the walk, the speech – but Langella balances it with what appears to be a sincere humanity. Even when the extent of Nixon’s own ruthless agenda becomes clear, along with his anger and self-loathing, in a drunken, late night phone rant to Frost, I felt more, not less, sympathy towards him.

All of this, by the way, is a roundabout way of saying I liked the film a lot – words I admit I never thought I’d write when discussing a Ron Howard film. I’m continually perplexed by the way Howard has, over the years, risen without trace to the point where people talk about him in embarrassingly glowing terms. Still, you can see why, maybe, he was drawn to this particular property. In the way George Clooney’s Good Night, And Good Luck was, to some extent, influenced by his own television background (and that of his father’s), maybe there’s some of Howard’s own youthful sitcom endeavours resonating here.

There might even be a contemporary imperative, too. By identifiying that Nixon went into Cambodia to find the “bamboo Pentagon”, the Central Office for South Vietnam (COSVN), and in doing so turned the Cambodians against America leading to the birth the Khmer Rouge, Morgan tacitly draws a parallel between Nixon and George W Bush’s own ill-conceived antics in Afghanistan and Iraq.

Interestingly, for a medium that’s mostly obsessed with the big explosion, the widescreen shot, this is a film whose outcome hinges on Frost’s understanding of “the power of the close-up”; and as one character says: “The first and greatest sin of television is that it simplifies, diminishes.” But it’s a big story, brilliantly told in this punchy, potent movie.

Frost/Nixon opens in the UK on January 9