The new Accidental Death of an Anarchist is a riot of laughs – but does it make us angry enough?

There is a fascinating role reversal going on in London theatre. Behind the elegant Corinthian facade of the Theatre Royal Haymarket, an ebullient satire on police corruption, Accidental Death of an Anarchist, has arrived by way of the Sheffield Crucible and the Lyric Hammersmith. Meanwhile Somerset Maugham’s The Circle, a Haymarket staple over the last century, has just enjoyed a triumphant revival at the off-West End venue of the Orange Tree, Richmond. Delighted as I am at the switch that puts political theatre in the commercial heartland, I came out of the Haymarket pondering how best to arouse an audience to a state of savage indignation.

The latest very amusing Accidental Death is a new adaptation by Tom Basden of a popular 1970 classic by Dario Fo and Franca Rame about the defenestration of a man in police custody. The story has been anglicised and updated but, since there is no reference in the programme to the historical case on which it is based, the young couple next to me understandably took it to be pure fiction. I reminded them that Fo and Rame were recreating a situation in which Giuseppe Pinelli, a Milanese railway worker, was falsely accused of a series of railway-station bombings and mysteriously fell out of a fourth-floor window at police HQ.

Writing shortly after the actual events, Fo and Rame were subject to endless harassment by the Italian cops. Fo himself told me the police did everything they could to try to stop the show and, on one occasion in Sardinia, beat up himself and other members of the cast and slung them into jail. “The whole audience,” Fo went on, “turned up in front of the prison, sang, shouted and protested the whole night through and what started out as an act of police repression ended up as a popular defiance of authority”.

The genius of Fo and Rame was that, in their play, they used comedy as a subversive tactic. They showed a maniacal character turning up at the cop shop, posing as a presiding magistrate and, in supposedly aiding the police, exposing their lies: Fo and Rame were simultaneously drawing on the traditions of commedia dell’arte and ingeniously circumventing censorship. Daniel Raggett’s new production adapts their tactics to the modern age. Daniel Rigby as The Maniac does endless funny voices and walks, brandishes a fake skeletal hand, puts his head through papier-mache scenery and hurls sweets panto-style at the audience. He is a fount of comic energy, the farce is played at furious speed and yet we are reminded that we live in a world where the police take selfies with murder victims and collusion and cover-up are standard practice.

But what impact does the play have on us? If I’m honest, I found that many of Basden’s accusations of police corruption were obscured by the production’s hectic pace. Only at the end did I feel stirred to genuine anger when on the back wall of Anna Reid’s set was projected a horrifying statistic: that “since 1990 there have been 1,862 deaths in police custody or following contact with police in England and Wales.” It is right that that is the production’s final statement but it also left me thinking that documentary fact is sometimes more potent than theatrical fabrication.

Related: Accidental Death of an Anarchist review – a riotous satirical farce brought bang up to date

The most persuasive indictment of the police I have ever seen was The Colour of Justice, which Richard Norton-Taylor edited from the Macpherson inquiry into the killing of Stephen Lawrence and which was staged at the Tricycle, now the Kiln, in 1999. Layer after layer of negligence and incompetence was revealed adding up to a devastating portrait of a police force later dubbed “institutionally racist”: only this week further evidence was uncovered of the police’s failure to prosecute a sixth suspect in the Lawrence killing.

I am not denying for a moment that comedy can be a potent theatrical weapon or that Fo and Rame’s play was, in its time, incredibly brave and bold. Seeing it in its latest incarnation, however, I felt that, for all the ingenuity of Raggett, Basden and Rigby, there was slightly too much sugar and not quite enough pill.