This time last week, Peters was in Edinburgh directing a very different kind of TV star, Denise Van Outen, in her Jackie Clune scripted solo show, Blondes, and expounding about a new wave of musical theatre on The Culture Show.
Somewhere in-between the two, Peters has managed to fit in two days filming on a new big screen version of Gulliver's Travels with Jack Black.
Peters will be jetting back to Edinburgh this weekend, however, for two very special mid-morning Question and Answer sessions, designed specifically with Wire fans in mind. That these are set to take place in The Underbelly's biggest space, The Udderbelly, is testament to just how much The Wire - the five series of which have only just been aired on terrestrial British television - has tapped into the public consciousness in a way that more generically bland home-grown fare in its current state will never manage.
While Peters is enjoying reaping the benefits of The Wire's status, there are plenty more strings to the bow of a man who takes his assorted crafts very seriously indeed.
As the writer of hit musical Five Guys Named Moe, Peters is about to celebrate the show's 20th anniversary with a revised revival.
Peters is also set to start work on a brand new show by Simon, which, following The Wire and a previous show, The Corner, will be the third collaboration between him and this most fiercely intelligent chroniclers of American life today.
It's The Wire, however, despite its cancellation after five series, that is as fresh in Peters' mind as it is for its umpteen converts still tuning into the show three late nights a week. Lester, however, wasn't the part Peters originally auditioned for.
"I put myself up to play Lieutenant Daniels," he reveals, "so when I didn't get it, but was asked to play Lester instead, I was initially disappointed, because I thought he was someone I didn't want to be. But then he turned out to be the man I wanted to be when I grew up.
"As a character, Lester started out as a man who'd been sidelined for doing the right thing. Fortunately the writers developed that, so by Series Five we saw him as something of a rebellious character. He's a bulldog, who once he finds something he'll hold onto it and won't let go.
"I was a bit dubious about some of the developments in Series Five, but David asked me to stick with it, which in the end I was glad to do. I see Lester as a man who wanted to do his best within the law."
For the few who haven't discovered its magnificence, The Wire is set on the streets of contemporary Baltimore, where, from its opening framework of the war between police and drug barons on the street, the programme pans out to take a hard-nosed look at the police, politics, trade unionism, education and poverty in an epic manner that makes the run-down city its star. Peters confirms that The Wire's seriousness and scope runs counter to perceptions of cynical producers only interested in peddling trash.
"The Wire isn't just good storytelling," he says. "It's intelligent. It appeals to people's intellect rather than the emotional sound-bites they're often fed, so you see one episode and it's like a chapter of a good book that makes you want to get on to the next chapter.
David is dealing with certain social issues in a way that treats the viewers with respect. People are a lot smarter than they're given credit for, and they don't want things that are dumbed down."
Which brings us to Blondes. Of his Edinburgh experience this year, while Van Outen's show has been scorned in some quarters, Peters is fulsome in his praise for its star.
"She was great," he says. "It took a while for Denise to find her feet, but she's got her own fanbase who expect certain things of her, when in actuality she's an unknown quantity who's an awesome talent.
"Sadly no-one seems to want to support that, but she can sing, she can dance, she can act and she can present. She could be the Shirley Maclaine of England if she wanted to be, but she's playing to an audience she's never played to before, and that's tough."
Peters grew up in New York, where he knew from the age of 12 that he wanted to be an actor. At that time in the 1960s, the British theatre scene monopolised Broadway.
"My career began in England," he says. "My first major role was in the west end with Ned Sherrin. I was thrown straight in the deep end, and sometimes if you've not been to drama school, that can make you feel insecure, but I was always trying to learn and to extend my craft, and I still do.
"I wanted to tell stories, and all these different talents are needed for that, so I would enrol for classes at the National Theatre, and learn about how to use the voice and how to use the body.
As a stage actor, Peter appeared on Broadway in The Iceman Cometh and Chicago, and on the west end as Porgy in Porgy and Bess. Peters was nominated for a Tony award for Best Book of a Musical for Five Guys Named Moe, which first appeared in 1990.
"I'd been doing a lot of work in revues," Peters remembers of the show's origins, "and when I had the idea for Five Guys Named Moe I approached Ned Sherrin, who I'd been doing all these shows about different composers with.
"But he said I knew enough about these things to be able to do it on my own. So if there's anything I fell into it was the writing, and I'm still learning about that. For its 20th anniversary we may change some of it, but if that doesn't work, that's okay, and we can just do it more or less the same."
The new David Simon series will be set in post Hurricane Katrina New Orleans.
"It's about the rediscovery of culture by musicians post Katrina," Peters says. "I play a bass player, and I think the programme will be as rich as The Wire, and a challenge for any actor. Our craft is important to society, and always has been.
Clarke Peters will be doing two Q&A sessions at The Udderbelly, August 28-29, 11am
The Herald, August 28 2009