Tom Davis is fast becoming a familiar onscreen presence. The hulking henchman Davus in Plebs, he's also Felix, Cockroaches' transvestite apocalypse survivor and the burly, bare-knuckle boxing Khloe in Keith Lemon's Big Fat Gypsy Kardashians. Appearing in the likes of Uncle, House of Fools and The Life of Rock With Brian Pern, the 6'7 sometime stand-up and former drag queen is comedy's go-to guy for intimidating muscle with a vulnerable underside.

For his first lead role though, he's chosen something more demanding. As the growling, hard-bitten but deeply insecure DCI Fleet in Murder in Successville, he's grappling with one of TV's weirder hybrid formats. Like Stella Street with a whodunnit element, character comics such as Cariad Lloyd, Colin Hoult and Marek Larwood improvise as celebrity homicide suspects Darcey Bussell, Gary Barlow, Boris Johnson, Jimmy Carr and Justin Bieber.

At the same time, Sleet is accompanied each episode by a genuine celebrity – such as Dermot O'Leary, Radio 1's Greg James or Dragon's Den's Deborah Meaden – playing a rookie cop who must find the killer. Sticking to the scripted plot while ad-libbing around the celebrity's interjections.

'I've never done a job where your mind is so in it, you've got to be on the whole time,' explains Davis. 'The main thing about improvisation is listening, being able to keep up and making sure you've always got something to say'.

Naturally, when the no-nonsense Meaden challenges Sleet's old school sexism or Made In Chelsea's Jamie Laing seems 'genuinely worried he's offended me', it's hard to keep a straight face. 'There's a bit in Louis Smith's one where I couldn't hold it together at all,' he recalls. 'I've always been a terrible corpser in anything I've done. And it's a lovely part of the show keeping it in, it's quite infectious.'

Returning in Plebs and The Keith Lemon Sketch Show soon, and with a role in the Bad Education movie spin-off, Davis 'just loves being on set, dicking around for a living. I count myself very lucky.'

Murder in Successville premieres on BBC Three, Wed 6 May.