All That Fall, Jermyn Street Theatre, London Scenes from an Execution, NT Lyttelton, London Desire Under the Elms, Lyric Hammersmith, London

This has to be major news: a play by Samuel Beckett that has never been staged, till now. Check out the casting, too: Eileen Atkins and Michael Gambon, no less, directed by Trevor Nunn. A queue of theatre fans, hoping for returns, was already snaking up the street last week, outside Jermyn Street's off-West End producing house.

Yes, but hang on. There's a reason why no playhouse has hitherto presented All That Fall. It's a radio drama, broadcast by the BBC in 1957. Still, you may say, that's no less reason to be enthused. This episodic journey play – decrepit Mrs Rooney traipses along a country lane, encountering locals then escorting her blind husband back from the railway station – is a work Nunn claims to have waited years to mount. So, he surely has some brilliant ideas on how to bring it to the stage.

Sadly not. The set is a drab black box with a bunch of old-fashioned microphones hanging overhead, The cast only half-pretend to be making a recording. They're in 1950s costumes, with Atkins's long-faced Mrs Rooney, blinking wearily, in baggy cardigan and brown felt hat. Everyone, though, is still script-in-hand, making this little more than a play reading. To call it semi-staged would be generous. Demi-semi-staged perhaps.

Nunn follows Beckett's tongue-in-cheek catalogue of sound effects pretty much to the letter: twittering birds, mooing cows, dragging footsteps, a trundling cart, a car horn, steam trains. These are pre-recorded, so you don't even get the fun of watching DIY creativity.

There's a bit of mime. Atkins sways on the spot, in synch with the amplified footsteps. There's also a car door onstage so we can see the absurd struggle involved in hoisting Mrs Rooney into the passenger seat. However, it would have been funnier left to the imagination. Nunn hasn't, visually, honed the farce.

It's sorely disappointing to think this production is from the same man who made physical theatre seem so inventive and witty in his staging of Nicholas Nickleby three decades ago. That said, someone from Broadcasting House should record Atkins and co. All That Fall is slightly scrappy and meandering, but Atkins's character has some splendid, quirkily poetic and comically gloomy lines. Also, though his Irish accent wobbles, Gambon's Mr Rooney – towering, in thick specs – has a scary temper, and gives the plot a startlingly psychotic twist at the end.

Howard Barker's Scenes from an Execution marks the sexagenarian British dramatist's belated National Theatre debut. Barker has long had a cult following, idiosyncratically running his own troupe, The Wrestling School. His plays have been challenging, violent, deliberately anti-entertaining and elusive.

Galactia, the artist-heroine in Scenes, is a barely disguised self-portrait. She's a non-conformist painter (a pursuit that features on Barker's CV), living in 16th-century Venice. Radically depicting the Battle of Lepanto's gruesomeness, she is punished by the Establishment, as embodied by the doge and a cardinal. They had commissioned a triumphal canvas. Ultimately, though, they switch tactics, undermining her rebel status by embracing Galactia rather than ostracising her.

It is ironic, on a meta-level, that Barker has been brought into the NT fold with this very play, a piece far less radical that his reputation might lead you to expect. It tells Galactia's story straightforwardly, it isn't hard to follow, and it manages to be satirically amusing too.

Leaving aside the major hitch on press night, when the huge, sliding walls of Hildegard Bechtler's set got jammed, Tom Cairns's production is perfectly watchable, with a wonderful central performance by Fiona Shaw. At once vibrant and relaxed, her Galactia is more charmingly boho than self-centred, striding around in a scruffy tunic, or lolling barebreasted in her studio. William Chubb is contrastingly frosty as the cardinal and Tim McInnerny, as the doge, is fantastically volatile, sometime cool as a cucumber, sometimes a sweating bag of nerves.

Lastly, why are there so few stagings of Desire Under the Elms, Eugene O'Neill's 1920s tragedy set on an isolated New England farm? Granted, it has its faults – the tragic climax is narratively rushed and the aggro between the old patriarch Ephraim and his bridling son Eben is heavily indebted to Euripides and Freud. But Sean Holmes's production is enthralling, echoing with melancholy bluegrass guitar. Denise Gough is riveting as Abbie, the aged widower's new bride, with big glinting eyes and tousled blonde curls. Hungry for property, her Abbie amazingly manages to be calculatingly seductive yet never clichéd, gradually revealing a desperate vulnerability. Though Morgan Watkins, as Eben, isn't so complex, their burning desire for each other is electrifying, as they dart between cramped attic bedrooms. Set designer Ian MacNeil's farmhouse – a jigsaw of spinning chambers – boldly mixes stark modernism with battered period furnishings, while Finbar Lynch's Ephraim sounds almost biblical, his rustic dialect infused with a haunting lyricism. Recommended.

'All That Fall' (020-7287 2875) to 3 Nov; 'Scenes from an Execution' (020-7452 3000) to 9 Dec; 'Desire Under the Elms' (020-8741 6850) to 10 Nov

Hurry to catch Simon Russell Beale in Shakespeare's riches-to-rags saga Timon of Athens, updated to our era of fat-cat bankers and the Occupy movement, at the NT Olivier (to 31 Oct, and in cinemas nationwide 1 Nov). Beautiful Burnout, Frantic Assembly's high-energy depiction of boxing – part drama, part dance – is at the Artsdepot in north London this week (Tuesday to 19 Oct).