Sitting in the corner of a central London restaurant in John Lennon-style pebble glasses and a leather jacket, Clarke certainly goes largely unrecognised. But it may not remain that way for long.
He will soon be rivalling Carol Smillie for TV ubiquity. Last week, he had a major role in i.d., a Screen Two film about football hooligans. Next week, he plays one half - Colin Buchanan is the other - of Reginald Hill's odd-couple detectives in a new series of Dalziel and Pascoe on BBC1. And soon after, Clarke will be starring in a new BBC drama called The Locksmith as well as A Respectable Trade, a new BBC serial on slavery. He will probably be reading the news before long.
Eric Abrahams, an executive producer on Dalziel and Pascoe, reckons that the curmudgeonly copper may be "that key role that's going to propel Warren into the major film circuit. He's been very underrated and underexposed.
"He's that really rare thing," Abrahams enthuses, "a heavyweight actor with a gift for comedy. His face is able to convey menace, pathos and humour from one second to another - and sometimes all at the same time. When he plays Dalziel, he gives the impression of using a four-letter word every other word - even though he doesn't. It's the `Psycho principle': it's not what you show, it's what you prime the audience to imagine. Therein lies Warren's skill."
Clarke was on the verge of making it big as long ago as 1971, when he played one of Malcolm McDowell's dastardly henchmen - or "droogs" - in A Clockwork Orange. He still remembers with awe working for director Stanley Kubrick. "We'd get in at 7.30 in the morning," Clarke recalls, "and the set would be cleared. Then Stanley and we four droogs would improvise all morning. In the afternoon, we'd shoot just one minute.
"Stanley was doing Mike Leigh before Mike Leigh was born," Clarke continues. "He'd say, `Warren, I don't know what dialogue to have in the milk-bar scene. Can you write some?' He'd give us freedom to invent."
Like the droogs, Dalziel is not an especially appealing character. He is more given to shouting and swearing than caring and sharing. Indeed, after complaints about the first series - the show was featured on Biteback - the BBC has toned down Dalziel's misanthropy for the second.
He's still not going to win any New Man of the Year awards. In "A Killing Kindness" from the new series, for instance, a right-on lawyer becomes exasperated with the detective's neanderthal attitudes: "I thought all that offensiveness was just an act," she rails, "but you're really as small-minded as the rest of them."
Abraham, for one, is unrepentant about Dalziel's unreconstructed world- view. "In this age when PC is all the rage," he argues, "Dalziel is this wonderfully human, non-PC character who articulates views that we can only think. He tells it as it is. There's too little of that. We're fed up with fashionable PC programming. Life's not like that, and audiences are quick to spot that."
Clarke is not going to disagree with any of that. "Dalziel is a dinosaur," he opines, "but I know that they exist because I've got mates in the force who tell me they do. One of the reasons I did the series was because I loved the fact that he doesn't bow to liberal views of society. He's this bloke from the North who's farting, scratching and behaving badly with women"
Doesn't he worry, though, that all these rozzers behaving badly will offend people? "That never worries me," Clarke booms. "In fact, that was one of the biggest magnets. On Richard and Judy, I said, `Dalziel gives me the chance to stick my finger up', and then I stuck my finger up. Judy went `Ooo', and there was an outcry from viewers. I even appeared in the Daily Express. I love all that."
`Dalziel and Pascoe' begins next Saturday on BBC1