The playwright James Graham has drawn flak from some commentators for meddling in real events as they are unfolding. In his TV drama Brexit: The Uncivil war, which aired this week, Graham uses the real world as his set but gets his facts about the real world wrong, say some critics.

Better perhaps for a playwright to avoid such imbroglios by drawing material from deep in the past. Knowing the details of his material had long since been forgotten, Shakespeare was free to shape a character or a plot at will to reveal universal truths more enduring than mere facts. And he knew better than anyone the role of fiction in exposing facts. Didn’t Hamlet say “the play’s the thing wherein I’ll catch the conscience of the king”? But can a play really be wrong? Bad, for sure. But a play is by its very nature fiction presented by actors. As a journalist I have often cringed when drama tries too hard to interest audiences in current events. Bankers dancing on desks during the West End play Enron was excruciating.

But some years back, when Tony Blair was in power, the greatest journalistic story of my life fell into my lap, and I began to see things differently. At that time my husband was the prime minister’s chief of staff; it was the run-up to the Iraq war, and the inside story of that political earthquake spilled into our family home at every hour of the day and night.

The voices of Bush and Blair and other leaders crackled over antiquated “secure” phones strung up in our bedroom, papers spilled from red boxes and, along with dinners at No 10, I gained extraordinary insights into what was taking place inside Blair’s “carapace”, as he called his cabal of loyal aides.

But, precisely because I was inside the carapace, I couldn’t write newspaper articles about what I was witnessing without ending up at both the Old Bailey and the divorce court. Then I realised that the story I was gathering was in any case better told as a play. The truth about why Blair made the disastrous decision to go to war lay as much in character as in errors of intelligence or policy, and character was best shown in dialogue set-up in scenes played by actors, not laid out in text.

And this was real-life drama. No piece of journalism could capture the moment when Bush’s voice crackled out in the bedroom, telling Blair he was ready to “kick ass” in Iraq and urging him to have “cojones”. “Yeah,” said Blair with a nervous laugh.

And only a drama could capture the scene at a No 10 dinner when, even as the Iraq Survey Group was reporting long after the war that no weapons of mass destruction had been found in Iraq, Blair’s most loyal intelligence chiefs said they would still be “proved right”. That was the moment to have staged my play to its full effect. But I had barely written a first draft.

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Graham, or his directors and producers, were right to stage this Brexit drama when they did. Just as it was broadcast, showing the leave campaign devising its winning slogan – Take Back Control – the political order collapsed further, our leaders never so out of control as they headed to the cliff edge.

Nor has any piece of journalism bettered Graham’s focus-group scene in portraying how the poison of Brexit has set ordinary people against each other, or exposed how easily our feeble leaders were led by opportunistic apparatchiks.

Setting a play against a backdrop of real events certainly demands perfect pitch – authenticity if not factual accuracy – precisely to avoid a discordant clash with the real world. Casting Benedict Cumberbatch as Dominic Cummings, the man behind the leave campaign, has been criticised as a stunt to entertain, and certainly risked shattering that authenticity by giving Cummings a Sherlock-like allure this backroom bully lacked.

The failure of journalists to present the truth about Europe and our relationship with it is much to blame for the mess we are in today. And Boris Johnson can take the accolade of journalist fiction-writer in chief, having honed his poisonous skills as the Telegraph’s Brussels correspondent.

More power to the elbow of any writer – dramatist, journalist, film-maker – who is prepared to try to bring this impossible story into focus in time to make our leaders see sense. Sadly the message is that it’s already too late because the poison has taken hold of the body politic: focus groups, apparatchiks, Dominic Cummings, Boris Johnson, Sherlock Holmes – the lot.

• Sarah Helm is an author and playwright. Her play Loyalty was staged at the Hampstead theatre in 2011