When, in the last election campaign, the Tories' ardent supporters at the Sun newspaper accused Jeremy Corbyn of threatening to drag the country back to the 1970s, they were ironically evoking the decade of their own first triumphant incarnation in tabloid form.

It's also a period in which the 35 year-old playwright James Graham seems entirely at home. Having written This House about the hung parliament of 1974, he now turns his attention to the year 1969 when an "Australian sheep farmer" called Rupert Murdoch bought a failing broadsheet newspaper - and transformed it into the super soaraway newspaper that has shaped the nature of modern Britain.

Graham sees this as the moment the country changed, when the deferential old order with high ideals and a sense of responsibility about the vision of the world it portrayed was replaced by the rule of the market, a pandering desire to give the people what they want, and a sense of newspapers as no better than chip wrapping. And this is the world he enthusiastically - and sympathetically - portrays in a production that vividly captures all the energy as well as the excess of the era.

It opens with a sound - the clatter of typewriters - and two men, emerging from the spotlight, to tell each other a story. One is Murdoch (Bertie Carvel), his head jutting like a tortoise, his voice silky smooth, with just the hint of an accent. The other is Larry Lamb. Yorkshire-born son of a blacksmith (tough-talking Richard Coyle) full of the wisdom of Fleet Street, the lore of how to tell a tale. As they circle one another over dinner (the first of three riveting encounters that punctuate the play), it's clear that what they share is a sense of exclusion from the British establishment and a desire, in Murdoch's words, "to create a popular paper for the masses. One that can unleash a part of...the British character that has never been tapped into, but is there, yearning for stuff."

And then they are off, through a compressed and much-adapted history of the Sun's first year as it seeks to overtake the Daily Mirror as the best-selling paper in the world. Bunny Christie has provided a wonderfully adaptable setting, an acting space piled with desks upon which the characters climb and scenes - including an explanation of the old-style of hot metal printing, controlled by the unions as an ancient rite - unfold in fluid succession.

On screens at the rear, headlines flash up, or papers rattle by as if on a printing press. As the mood darkens and the world changes, ink floods down and blocks out of the images.

Rupert Goold's direction incorporates song and dance as Lamb recruits a motley crew of journalists and begins to develop his vision of giving people what they want. (TV! Sex! Free gifts!) The first half, is a riot of anecdote and zinging dialogue. Tim Steed, as the uptight deputy editor Bernard Shrimsley - "I should warn you that nobody likes me" - has a lot of fun with his character, and although the rest of the cast never really escape from the caricatured strait-jackets assigned them, they play their roles with zest.

The second half is more problematic, as Graham uses a shocking case where a woman is kidnapped and killed having being mistaken for Murdoch's wife as a means of exploring the amorality of the Sun's reporting. It's fascinating and terrifying but it almost derails the play, and the subsequent explanation of the arrival of Page Three feels both under and over explored, as it is asked to carry more weight than it possibly deserves.

The scene between Coyle and Pearl Chanda's hesitant Stephanie is beautifully written, however, and the supple power of Graham's writing always has the capacity to wrong foot expectations, to frame difficult questions. What he's really interested in is the stories that we tell ourselves about who we are; the narrative of our national character and the dangers of always trusting the majority opinion speak loudly to our own times as well as to the decades gone by.

But what makes Ink ultimately unmissable is Carvel's performance as Murdoch. It would have been easy to turn such a hate figure into a caricature, but Carvel gets under his skin. Every time he appears, his arms stiff, his body tensed, coiled with the sense of his own power, he sends a jolt of electricity through the entire theatre, perfectly encapsulating the dangerous disruption that Murdoch brought to British society.

Ink runs at the Almeida Theatre until 5 August.