When historians look back on Barack Obama's first and second presidential elections, they may see some commonality. Four years ago, the country's first black White House candidate was smeared with all sorts of allegations. The would-be president was not born in the US. He was a mole. A socialist – no, make that a communist. Barack was gay. Barack was a Marxist. And a Muslim too.

Now the same myths are rumbling through the country's bars, online forums and, worryingly, major news outlets. And this time there is a list of failed promises – on Guantánamo, universal healthcare – to add to the attack, while the personal claims seem to be yet more torrid (this week's most bizarre is that "Obama's mother was a porn star").

It is against this backdrop that new playwright Rashid Razaq is staging his debut production, based on Obama's college days at Columbia, New York. Provocatively titled The President and the Pakistani, it revisits Harlem, 1981, when "Barry" Obama was living with his alleged party-loving, drug-abusing, illegal alien Pakistani friend, Sohale Siddiqi.

"They had an odd-couple relationship," says Razaq, a reporter for the London Evening Standard, showing me a picture of the pair sprawled on a mustard yellow sofa, a leather-jacketed and polo-sweatered Obama kicking back with an impressively moustached, skinny Pakistani. In the play, Siddiqi has been renamed Salim "Sal" Maqbool; in Obama's 1995 autobiography, Dreams From My Father, he was recreated as a composite character named Sadik, mentioned in only a few pages.

"Sal is a cokehead", says Razaq, who admits he has never spoken to the person on whom the character is based. "He has manic, nervous energy while Barry is the stable, secure, sensible guy. But there is a real closeness between them and hopefully that comes across." At heart, Razaq's play is a studied 80s bromance.

But what would Siddiqi himself make of it? When I track down Obama's former room-mate, who now works for Getty Images and lives in Seattle, he is reluctant to speak. Not least, he says, because a reporter from Associated Press "got his interview by barging in unexpectedly at my workplace in spite of my declinations" during the last campaign cycle.He says the reports of his drug use have been wildly overstated: "I was never in 'rehab'," he emails, "I simply curtailed drugs." It is true, however, that in the late 1990s, as state senator of Illinois, Obama wrote him "a personal reference, stating that he knew me" when Siddiqi was applying for jobs in the dotcom industry. Their lives had naturally drifted apart by that point, but a solid bond remains. Siddiqi still refuses a steady stream of press requests to talk about his old friend, including the offer of $50,000 to talk to one anti-Obama film-maker just a few weeks ago.

I send Siddiqi a copy of the script and ask him what he thinks. He says he feels "helpless" about the play. "The portrayal of 'Sal' as a clingy and dishonest roommate is completely off the mark and makes me cringe," he writes.

"Obama was exceptionally kind and considerate of others which I considered to his own detriment – the play got that part correct," he says of his time spent living with the president in a shabby apartment on East 94th Street. It was a lease that Siddiqi, who was an illegal immigrant when he met Obama (having overstayed his tourist visa), had lied to win, despite the cockroaches, "like plump dates", scuttling across the apartment floor. Siddiqi confirms that the young Obama, a high school pothead, "was lighthearted and fun-loving for the first half of our cohabitation and grew serious later". He himself, meanwhile, was preoccupied with "assimilating to my new environment [US], getting rich legally, socialising with friends, meeting women. Our cohabitation was on a temporary basis with me hoping to move to more comfortable surroundings and he wanting to live closer to Columbia."

Syrus Lowe (Barry Obama) and Junaid Faiz (Sal Maqbool) in rehearsal for The President and The Pakistani. Photograph: Michael Lidbetter

Does it matter if the play is inaccurate? "It wasn't about showing [Obama] doing drugs and making it shocking and sensational," says Razaq. "Without it sounding sinister, he has just been a very ambitious, driven guy and we see the beginning of that in this play." We are talking in the compact, cheaply refurbished west London studio where his cast of two, Syrus Lowe and Junaid Faiz, are rehearsing. Mild-mannered but sure-footed direction comes from Tom Attenborough, son of Michael Attenborough (artistic director of the Almeida theatre, London) and grandson of actor and director Richard.

I wonder if Razaq agrees that representing a living president during the busiest period of electioneering is political in itself. "All theatre is a political act to some degree. We're just grabbing it by the balls," he says. Emphasising his right to artistic licence, he says he drew inspiration from Obama's own book and scoped David Maraniss's biography, Barack Obama: The Making of the Man, published earlier this year, for further detail.

When we meet "Sadik" in Dreams From My Father, he is ushering Obama into his flat as a woman in her underwear cuts up lines of cocaine on the kitchen table. In Maraniss's doorstop of a book, Obama first meets Siddiqi at a New Year's Eve party in San Francisco, the young, gangly, would-be president greeting his future roommate with pitch-perfect Urdu, asking: "How are you, Boss?" It was a phrase he had picked up from his best buddies at Occidental College in California – Pakistani students Imad Husain, Hasan Chandoo and Wahid Hamid who, like Siddiqi, were part of Karachi's wealthy elite. So close were the group that Obama went to Pakistan with them for a three-week holiday in 1981, staying with Hamid and Chandoo's families.

Maraniss argues in his book that the group has distanced itself from Obama for fear of hurting his presidency, but they remain friends: "The Pakistanis were a fun-loving bunch," he laughs, talking on the telephone from Washington DC, "but they were intellectuals." Despite their party harder reputations, the three went into highly paid corporate finance: Husain is a Boston-based banker; Hamid works for one of the world's biggest private equity firms in Dubai; and Chandoo – who is recorded to have fundraised some $50,000 to $100,000 for Obama's current campaign – is a financial consultant, living with his family in upmarket Westchester, New York.

Camp Obama plays all this down, fearful of the Pakistani Muslim connection being used to taint their candidate. "A friend of mine did wonder if the play was about Pakistan now," says Syrus Lowe, who plays the young Obama, as we discuss the irony of one of the president's hallmark foreign policies: the covert US war against Pakistan, waged entirely through drone attacks.

Lowe says he likes to think Obama is "dropping those drones with a bit more conscience" than the average US president might. Maraniss is less circumspect. "The Pakistanis, in my mind, didn't shape him in any way but made this transitionary period of his life comfortable for him, as he was still learning what it was to be African American. They could see his ambition more clearly than other people; it was to them that Obama first said he wanted to be president one day."

The President and the Pakistani is at the Waterloo East theatre, London SE1, until 4 November.