If somebody drew a family tree of modern British comedy, Peter Serafinowicz would be hanging off every branch. He played Simon Pegg’s rival in Spaced, Pegg’s flatmate in Shaun of the Dead, he has starred in the sitcoms How Do You Want Me? and Hardware, and co-fronted the cult schools programme pastiche Look Around You.

And that’s just for hors d’oeuvre. This genial, striking Zelig-like figure has also appeared in Little Britain, I’m Alan Partridge, Black Books and umpteen other giggle-fests. Finally, however, he has got his name in the title. The Peter Serafinowicz Show is an instantly accessible half-hour, bundling together the madness [[ of Lucas and Walliams with familiar telly send-ups and pin-sharp parodies. The 35-year-old Liverpudlian gives a particularly good Paul McCartney impression.

It might be a typical format, poking fun at shows such as The X Factor and Who Wants to be a Millionaire? and getting predictable mileage out of bad wigs, prosthetics and fat suits, but, as the talkative comedian explains, it came about in an untypical way.

“I’d been in Los Angeles auditioning for various pilots, and while I was hanging around I shot some spoof showbiz reports with my girlfriend Sarah [Alexander, from Green Wing].” One was a story about John Lennon inventing the iPod in the Sixties (it looks like an old fridge because it is an old fridge), another was a report that the Oscars statue had had a makeover and now sported a shiny gold penis.

He put his clips on YouTube and soon they were being seen by everyone from his mum to TV’s top executives. “By the time I got home, the BBC, ITV and Channel 4 all wanted to meet me.” Which sort of makes him the Lily Allen of comedy? “Yes, I guess so. I don’t know of any other show that has happened in the same way, but I’m sure there will be more.

“Everything in TV is changing so fast. In fact we realised recently that television is the common thread in my series, so while it was born on YouTube it is also being nostalgic about television, wondering how these old programmes will survive when everyone will be able to watch everything at the click of a mouse.”

Things could have been very different. In America Serafinowicz had auditioned for the part of the writer/performer Tom Jeter in Studio 60 On The Sunset Strip. Had he been cast we would not be seeing his magnificent Michel Caine impression. In fact he did land the token-Brit part in a pilot of a Friends-type comedy, Our 30’s, but, thankfully for us, it didn’t go to a series.

Serafinowicz has clearly never been short of work and is never likely to be. If you somehow haven’t seen his face, you will definitely have heard his dulcet tones. He spent much of his twenties doing voice-overs. “New Ariel Ultra gets your whites not just nearly clean, but really clean!” That’s him. He has turned his tonsils to film trailers, too. “ Love, Actually – it’s the feel-good film of the year!”

His versatile diction also led to a nifty Star Wars sideline. He did Darth Maul in The Phantom Menace and then sent it up rotten as Darth Chef in South Park. “I love the first Star Wars films,” he says with glee, before confessing that he isn’t such a fan of the sequels. It was clearly a dream come true, then, that in his own show he got to wear Darth Vader’s costume. “I’m 6ft 4in and Dave Prowse who played him was 6ft 7in, so I had to wear a platform shoe, but I was very pleased with it.”

The BBC must be pleased with his series, confidently airing it on BBC Two at a time when new comedies often launch on BBC Three. “It makes me quite nervous and also makes me think it had better be good enough, I can’t let them down.” Fans who know Serafinowicz from his hipster outings might be sorry to see him doing something this populist, but the star-in-waiting is unrepentant. “It’s pretty mainstream, but mainstream doesn’t have to equal crap. We want to have as broad an audience as possible, but at the same time make something seriously weird.”

The Peter Serafinowicz Show, Thur, BBC Two, 9.30pm; see the YouTube clips at timesonline.co.uk/television

Editor's choice

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