Jack Thorne
Jack Thorne
© Dan Wooller for WhatsOnStage

On Sunday night, Jack Thorne accepted his fifth BAFTA award – which isn't too bad for a playwright.

That's how we tend to frame Thorne – lately expanded to 'Harry Potter playwright.'' The truth is, however, that he's just as much a screenwriter as he is a playwright. Anyone who wants to understand his work critically has to look at both art-forms. To make sense of Thorne's plays, you have to turn to his television – and vice versa.

Harry Potter and the Cursed Child might look like a departure for the writer of small-scale political plays like 2nd May 1997, a state-of-the-nation triptych about New Labour's landslide, and Hope with its embattled local councillors. Less so, for the writer of cracking offbeat sci-fi series The Fades, about dead souls stuck on earth, the cancelling of which still rankles.

Thorne's writing on Skins and This is England makes sense of his new musical Junkyard – all of them, in a sense, about teenagers carving out spaces of their own – and you'll find a motif of illness and disability running from his debut play When You Cure Me to his recent The Solid Life of Sugar Water, but it's worth factoring in his Channel 4 comedy series Cast Offs. You could even tie National Treasure back to Fanny and Faggot, seen at the Finborough back in 2007, given both centre on crimes committed against children.

How often, though, do critics cross-pollinate like that? Experts in our own art-form, we tend to stick to one field. Audiences do, but we don't often draw lines between them – at least, not with writers. Directors, yes; actors, yes; writers, not so much.

This weekend, I saw Lady Macbeth, largely because I happened to spot the screenwriter's name – Alice Birch. She's better known as a promising playwright. Her new one, Anatomy of a Suicide, opens at the Royal Court next month. Lady Macbeth's her first film.

Playwrights have long written for the screen, but we tend not to consider it critically

It is, however, pure Birch. A free adaptation of Nikolai Leskov's 1865 novel Lady Macbeth of the Mtsensk District, relocated from rural Russia to the moors of North East England, it follows a young woman (Florence Pugh), squeezed into the corset of an arranged marriage, as she starts an affair with a stablehand. It leads her to murder – and murder, and murder, and murder. Each death triggers another, as Katherine and her lover attempt to cover their tracks, and each is more heinous and more indefensible than the last.

It's a stylised script: stark, still and often silent. Birch made her name with a play about language, Revolt. She Said. Revolt Again, and precision is a hallmark of her writing. Her work is motored by feminism, and Lady Macbeth is a galling portrait of the prison of marriage in Victorian England (if not now). Yet, as in Revolt, the film's keenly attuned to the pecking orders of patriarchal hierarchies. Repressed by her husband and her father-in-law, Katherine rounds on her housemaid Anna, played, in a pointed anachronism, by the black actress Naomi Ackie.

Birch's play Ophelias Zimmer, written for Katie Mitchell, finds a young woman confined to her room, largely without speaking, abandoned by her lover. So Pugh's Katherine sits, silent, staring out of her bedroom window or falling asleep on the sofa, bored brainless by isolation. The whole film is unflinching, just as Mitchell's theatre can be. It lets actions speak volumes: hair is brushed aggressively, corsets are pulled tight and a suffocation plays out, excruciatingly, in real-time.

Today's playwrights are swinging between stage and screen much more regularly

This is a film steeped in theatre (and its director William Oldroyd is a former Young Vic associate), yet, this being Birch's screen debut, none of the reviews really find the reference points.

Playwrights have long written for both stage and screen. Harold Pinter penned 24 screenplays – some of his own plays, most adaptations of novels and short stories. Tom Stoppard has an Oscar for Shakespeare in Love, and David Hare wrote The Hours and, most recently, Denial. Both have small screen credits too: Parade's End for Stoppard, and The Worricker Trilogy spy-thrillers for Hare. (They are by no means alone.) Yet, none of these scripts wind up in collected works, and we tend not to consider them critically. All three men are, instead, defined by their theatre writings.

Perhaps it's a question of what counts critically. After all, we can shape a narrative around Jez Butterworth's plays, but it's hard to reconcile them with his sci-fi blockbuster Edge of Tomorrow or the Bond franchise. Likewise, all those young playwrights that have honed their craft writing for Holby City or EastEnders – how much should we take that into account. There's an assumption that screen work pays the bills, while stage plays make the artist. Or else, we assume that theatre allows a playwright's voice and vision to lead, where meddling producers and execs tend to twist pitches out of shape and send scripts off for rewrites. How much, then, can we ascertain from a screenplay?

How often do critics cross-pollinate like playwrights?

However, today's playwrights are swinging between stage and screen much more regularly – a product of the rise of new writing onstage and, as important, the shifts in television over the last decade. It's rarer and rarer to find a playwright swearing off screen altogether as, say, Caryl Churchill and Martin Crimp have done, and a new generation of playwrights are open to all art forms.

Mike Bartlett wrote last week's episode of Doctor Who, after two of his own drama series The Town and Doctor Foster. Lucy Kirkwood wrote The Smoke for Sky1, and James Graham, Channel 4's Coalition. Nick Payne's adaptation of Julian Barnes' novel Sense of an Ending hit cinemas this year.

How, then, do critics and audiences keep up? Because when Jack Thorne's winning BAFTA after BAFTA – not to mention when Tarell Alvin McCraney's winning the Best Picture Oscar – we can't stay confined to one art-form at a time.