The TV comic and stand-up, who hosts the Dave series as his popular character The Pub Landlord, said that like "all the best things", CFTM came about by chance.
"I was writing with a guy called Mark Augustyn, who is a writer and producer. We were writing a quiz book and it was taking a lot of effort," he told DS.
"We needed to do lots of research and it was driving us mad. So to take the edge off it, we said, 'Why don't we do this as a show in Edinburgh? We'll drink in the day, do the show and basically have a jolly'. I wanted to go to Edinburgh and not write a show, because that's a real ball-ache."
While up in Edinburgh, Murray was contacted by various TV producers and broadcasters, who believed the pub quiz performance could be transferred to the small screen. "We did the show, people were enjoying it and then Dave and various other people came along and said, 'Do you want to do this as a TV format?'" he said.
CFTM, which launches tonight, is a surreal quiz show like nothing else on television at the moment. A mixture of celebrities, daft prizes, bizarre questions and pub banter, it's the most original slant on the stale TV quiz format since Shooting Stars was launched nearly 20 years ago.
Murray was initially reluctant to make the shift to television, admitting that he had concerns about the programme being watered down for mainstream audiences. "In August last year, I actually said, 'Can everyone stop f**king talking about this as a telly format'," he revealed. "The moment you involve telly people you ruin it. You are into compromise territory and the usual thing is, 'We love what you do, now do something different', or 'We love that bit, but you can't say it'.
"So the whole show has come about by accident really, and those are the best things, I think. The things that come about by accident."
The comic was also more than happy to revisit The Pub Landlord, who he first debuted in the '90s. He claimed that, unlike other performers in the past who have found success with their comedy creations, he didn't get frustrated by his close ties to the burly, British traditionalist. "He's just a great character for holding up things that are daft and making fun of them," he said.
The prize on Compete For The Meat is a frozen chicken, while the runners-up get a bag of sausages. It might not sound like much, but Murray said that he found traditional quiz show offerings more unusual.
"I personally think there's something a bit perverse about people winning money on telly," he explained. "People who think all their hopes and dreams will be made if they can win £14,000 and clear their credit card debt. I think that's a bit weird.
"A chicken is stupid and frivolous, but they are playing for glory. Basically, people really want to win that chicken."
If the show becomes a success, Murray said that he is fully expecting the programme's catchphrase chant of "thick and slow" to be yelled at him in the street ("One of my kids has already sung it at me - it gets pretty annoying"), and he is already concerned about show mascot Mr Giblets - a man inside a giant frozen chicken costume - getting too big for his boots.
"The bloke inside Mr Giblets, he's like our Stig," he joked. "I can't tell you who he is and I'm not going to tell you who he is. And what will probably happen is that I'll end up with a book being written about me and how I was nasty to him."
Compete For The Meat airs tonight at 9pm on Dave.
> Read more TV news