The Aussie comic on his YouTube hit, why teachers are using his video and how his 'police-related activity' means he won't be touring the US anytime soon

Late last year, Aussie comic Aamer Rahman was considering giving up standup. He and his partner Nazeem Hussain were disbanding their political comedy double act, Fear of a Brown Planet. Hussain had got himself a TV show, but, although the pair had been a hit at the 2011 Edinburgh festival, 31-year-old Rahman felt "at the end with comedy. I thought, my audience is small, what I'm doing is too niche."

So, demob-happy at their last few gigs together, he performed a routine that didn't usually feature in the show. "A lot of white people say this to me," the riff began. "They say, 'Hey, Aamer, you get onstage and make your jokes about white people. Don't you think that's a kind of racism? Don't you think that's" – dramatic pause – "reverse racism?'"

Six months later, that routine has been viewed by more than a million people on YouTube, and Rahman's early-retirement plans are on ice. "In terms of the audience it's generated for me," he says, "it's beyond anything I've experienced before." Within a month of going online, the clip had been featured on Huffington Post, Buzzfeed and websites across the US. "Then it just snowballed and got me more attention than I'd gotten in a long time."

The attention is richly deserved: the "reverse racism" routine is a cracker. In it, Rahman imagines aloud what would need to have happened for the accusation to make any sense. He'd have to get in a time machine, he deadpans, and persuade the leaders of Africa, Asia and the Middle East to invade and colonise Europe. He'd have to "ruin Europe over a couple of centuries so all their descendants would want to migrate [to] where black and brown people come from". He'd have to initiate social systems that privileged black and brown people, while intermittently bombing white people's countries, and "saying it's for their own good because their culture's inferior".

One after another, Rahman stacks up these hypothetical conditions – or should I say part-hypothetical, given that they've already happened, just the other way round. We know that, and he knows that, as his world-weary demeanour hilariously betrays. "What I convey in the clip," he tells me, "is the exhaustion of having to have a pointless argument, of explaining this to people again and again." That said, Rahman claims the "reverse racism" tag never bothered him. "It's just a given that that's a silly accusation. But then someone very close to Nazeem and me made a comment along those lines, quite unexpectedly, and that was the day I wrote the joke."

Now, he says, "the number-one feedback I get from the clip is, 'I've been trying to explain this to my friend, or a colleague, for years – and now I just send them your video.' And I get emails from university professors who play it in their classes. They say, 'I didn't have to write a lecture; I just played this and the kids argued about it for the next 60 minutes.'"

That's the sort of routine it is – the kind (like Bill Hicks on advertising, say) that's so perfectly expressed as to be definitive, and so contentious that it raises hackles and whoops of enthusiasm in equal measure. It's also wholly in keeping with Rahman and Hussain's other work. In Edinburgh, they were like a breath of fresh air – two naturally funny young standups who were also unapologetically political. That shouldn't feel unusual, but it did. "When we started out in Australia," says Rahman, "it was novel to have two young brown guys doing very pointed, overtly political comedy. But we expected that to already exist in the UK. We were surprised it was still a novelty there as well."

Inspired by Hicks and Richard Pryor, Public Enemy and hip-hop, Rahman had never considered tempering his material for white audiences, or for mainstream success. "Nazeem and I never asked ourselves, 'Are people going to be shocked when they hear this?'" he says. "It was more, 'Are our friends going to think we're lame, or are they going to laugh?'"

Now the global YouTube community is laughing, too – although Rahman can't capitalise to the degree he'd like. For a start, it doesn't cost anything to watch the video. "I met someone the other day who asked me with a straight face whether I make a million dollars a year." He guffaws. "Great as it is to have millions of people watch the video, they watch it for free." He would like to tour the US, where the clip has reached its widest audience, but "visa issues due to some police-related activity when I was younger" are complicating things. (He was, and still is, heavily involved in activism, "mostly around refugees and immigration into Australia".)

Instead, there's London, where Rahman is about to perform for two weeks. But audiences shouldn't expect to see the "reverse racism" segment. "I've never done it on stage since [it was filmed]," he says. "People grumble if comedians do bits they've heard already, so I've had to decommission the routine. But that two-and-a-half minutes has opened more doors for me than several years of touring, so I'm not complaining."

• Aamer Rahman: The Truth Hurts runs 10-21 June. Box office: 020-7478 0100. Venue: Soho theatre, London.