The writer's political play This House has just transferred to London's West End, four years after it premiered at The National Theatre.
Asked what his next project will be, Graham told BBC News: "I'm working on a TV drama about the referendum campaign.
"I think [Brexit] is going to be the main occupying idea in all writers' heads for the next five or 10 years."
He added: "That doesn't mean necessarily writing a dramatic re-enactment of referendum night, I think it just means the new mood we're living in, which is very different, a bit scary, very divisive, very angry, very confused."
But Graham confirmed that his TV drama will "specifically tackle what happened" in the run-up to the EU referendum on 23 June.
The playwright has previously written a short play about Brexit for The Guardian as well as The Vote, a play set in a polling station, which was televised on More4 on the night of the 2015 general election.
His other credits include musical Finding Neverland - for which Graham wrote the script and Gary Barlow the music and lyrics - and Privacy, which made its debut on Broadway earlier this year starring Daniel Radcliffe.
This House deals with the struggles of the Labour government between 1974 and 1979.
It debuted at the National Theatre in 2012, and recently had a run at the Chichester Theatre before transferring to the West End.
The play's director Jeremy Herrin said he was "delighted" by the reaction the play has had.
"We haven't really changed much of it, James has kept the same script," he told the BBC.
"When we first did it, the audience's obsession was much more about the coalition government in 2010 and how that was working out, and now it's much more about what's happening in the Labour Party."
He added: "It's much more about dignity and honour in politics, and whether the procedure can reflect our natures.
"Particularly post-Trump, it feels like that's the big question in the production - is it possible to be a decent human being in a parliamentary framework? So the play starts to answer that question."
The Guardian's Michael Billington described This House as "enthralling" in his five star review of the play after its West End opening.
"Graham brilliantly captures the daily machinations of politics," he wrote. "The whole ensemble contributes to a thrilling play that both relives history and transcends it."
Writing in The Telegraph, Dominic Cavendish said This House is "the most intelligent, entertaining and informative political drama of this decade".
He added: "This House is a must for those who want to learn more (or be reminded about) the very peculiar workings of Westminster and its often quietly heroic occupants."
The play was described as "magnificently sharp and witty" by Fiona Mountford in The Evening Standard.
"Whoever would have thought that the intricacies of a minority government struggling to pass a series of bills would have been so engrossing?"
She added: "Both a treat and a triumph, this is a superlative night out in the West End."
Comedian Jack Whitehall, who also attended Wednesday evening's press performance, described it on Twitter as an "incredible, amazing production".
Culture Minister Matt Hancock said it was a "brilliant portrayal of 1970s political drama".
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Playwright James Graham has revealed he is writing a TV drama about the EU referendum campaign.