Comedian and activist Brand - who has long campaigned against the criminalisation of drug addicts - planned to challenge David Cameron on why the government has failed to reform drug policy.
But the prime minster rejected the interview offer.
So instead Brand interviewed Clegg - one of the most prominent critics of his own government's drug policy and probably the most sympathetic politician in Westminster to Brand's cause.
The result was a strange competition over which man could agree with the other more.
For several minutes in the BBC Three programmeRussell Brand: End The Drugs War, Brand and Clegg passionately laid out their - very similar - viewpoints on the policy which both feel politicians are failing to reform.
Clegg agreed forcefully with Brand that the prison system doesn't help to tackle drug addiction: “You’re right, it has to change because, like you rightly say, we’re housing people behind bars then simply just ejecting them into normal life and expecting them to find their feet again."
"It's patently absurd," Clegg added.
"We have an obligation, we have a duty to bring about change... it all takes so long," said Brand, while Clegg nodded and said "Yup".
“I think we’ll look back on it in 50 years time and think, 'What?'” said Clegg.
Amid hand gestures and raised voices, both men seemed to be united in their outrage.
Brand attempted to challenge Clegg on the fact that politicians are moving too slowly to change their approach to drugs.
“That’s what makes me sort of despondent about the political system – and I don’t suppose there’s anyone in the country who’s more despondent about the political system than you,” the comedian observed.
Here, Clegg was again on his side. “I totally agree with you," the deputy prime minister said. "There is a ridiculous, outdated, deeply sort of shriveled, unheroic cowardice in the British political class... where people will talk about reforming drugs when they're not in office, and the moment they get in offices like this they shut up.”
The harmony was almost broken when Brand pushed his point a final time, saying: “That’s just not enough Nick, it’s not enough,” and stressed the needs of drug addicts who are "struggling to get through the next three seconds."
But rather than arguing, Clegg conceded: “Fair enough,” before the pair laughed warmly and shook hands to end the interview.
Just in case there were any hard feelings, Brand can be heard saying: “I like you, I know you're a good man,” as they stand up to leave.