9. Dr William H Masters

Perhaps the real person that Sheen has impersonated most often, he played the gynaecologist and sex researcher through 46 episodes of the excellent Masters of Sex. Masters died in 2001, 12 years before the start of the show, but it’s clear from video available of the man himself, this is more of an artistic interpretation by Sheen than an out and out impression.

8. HG Wells

The BBC docudrama War With the World, in which Sheen took on the role of the pioneering science-fiction author, is hard to come by now – and with the disparity in age between the Wells he plays and the age of the real Wells by the time he was being captured on film, it’s hard to judge just how accurate the portrayal is. Nonetheless, the scene where Sheen’s Wells meets up with Roger Heathcott’s Stalin certainly feels authentic.

7. Graham Norton

There’s perhaps a touch too much camp, and a splash too much hand waving in Sheen’s take on the chatshow host – but it beats Norton’s attempt at embodying Katie Price hands down. And the slump back in his chair is spot on.

6. Jeremy Dyson

Nothing to do with vacuum cleaners – this is a little known Sheen gem as he pops up in The League of Gentlemen’s Apocalypse (2005) as the fourth gentleman, writer and director Dyson. The man himself is the only one of the League not to star in either the shows or the film, so it’s left to Sheen to take on the role when the inhabitants of Royston Vasey invade the real world to assault their creators. The frizzy hair is on point, the wardrobe exactly right, and his Yorkshire twang, while perhaps a tad too high-pitched, has Dyson’s intonation to a tee.

5. Kenneth Willams

The comedian Williams is infinitely imitable, but nobody has done it better than Sheen with his Bafta-nominated turn in the BBC Four’s Fantabulosa! (2006). Sadly it’s not on iPlayer at the moment, but if you can track it down do – whether enjoying a cup of tea, or camping it up in Carry On, Sheen captures all the camp delights of the real Williams.

4. David Frost

Playing one of the most well known TV presenters in the country, first on stage (2006) and then on screen, in Frost/Nixon would be daunting for some. But Sheen nails Frost’s amicable on-screen demeanour and his steely off-screen determination. He never really looks like Frost – but the combination of well known vocal tics and physical traits convince (even if Frank Langella rather steals the show with his version of the disgraced US president).

3. Chris Tarrant

There’s almost nothing wrong with Sheen’s brief, if crucial, role as Tarrant in ITV’s Quiz. Watching the drama alongside footage from the episode of Who Wants To Be A Millionaire that it recreates, it is evident just how much home work the actor has put in (along with wardrobe and makeup). If there’s one criticism, it’s that he’s slightly more nasal than the real Tarrant – but that’s a minor quibble.

2. Brian Clough

The look, the voice, the perfectly recreated wardrobe – everything is right about Sheen’s performance as the iconic Nottingham Forest manager Brian Clough in The Damned United. The film focuses on Clough’s unsuccessful sojourn at Leeds United (2009), and Sheen is in almost every scene. Where some impersonations can be showy, this never feels anything but natural, and entirely convincing. Clough was a man of great wit and intelligence (especially in these days before his relationship with alcohol somewhat dimmed his senses) and this performance lovingly captures the great man. It’s only when going back to watch some of the real-life interviews recreated that the sheer brilliance of Sheen’s impression becomes evident.

1. Tony Blair

The first of Sheen’s appearances as Blair came in Peter Morgan’s 2003 Channel 4 film, The Deal, when Blair was still prime minister. Playing a man dominant in public life while not tipping over in to charicature was no easy feat – but Sheen’s eerily accurate portrayal was never distracting. Alongside David Morrissey’s uncanny rendition of Gordon Brown, Sheen stole the show. In this and two subsequent projects, 2006’s The Queen and 2012’s The Special Relationship, he has presented a version of Blair who, while never overly warm, was always human and sympathetic. And that’s a sign of just how good an actor he is – he doesn’t just “do impressions” he becomes people, to the extent that he recently told the Guardian that, despite his strong political views, he finds it hard to judge Blair objectively: “There’s still a little bit of me that when I see him or read about him that I’m sort of seeing myself. That’s a weird thing to have.”