Richard III, Old Vic, London<br/>Lullaby, Barbican Pit, London<br/>The Beggar's Opera, Regent's Park Open Air Theatre, London

Spacey swivels between hand-twirls and hollering in Mendes's 'stagey' production

It says “NOW” in huge letters, projected overhead, at the start of Richard III, directed by Sam Mendes. With Kevin Spacey as the malign crown-snatcher, this should be a triumphant climax for the Bridge Project, Mendes’s three-year series of transatlantic Shakespeare productions, co-presented by the Old Vic and the Brooklyn Academy of Music.

This modern-dress Richard III is also accompanied by programme notes stressing how the eponymous villain is astonishingly like Gaddafi and Mubarak. It’s soon apparent, however, that Spacey’s Richard (with a veering British / American accent) resides in Nowheresville and a time warp where the Duke of Clarence’s jailer wears a pinstriped suit, yet his prison cell is furnished with a wooden butt of malmsey. The ailing King Edward IV is attended by a nurse from the Edwardian era, as in Edward VII. A case of chronic dyslexia? And Spacey’s Richard, while feigning chapel prayers in a monk’s cowl, speaks with his spin-doctor, Buckingham, via a video link. That’s a strained concept played for laughs.

Spacey has electrifying moments, none the less. Slouched in an office chair with a crumpled paper crown, like a sardonic outcast from a Christmas party, he deliberately downplays Richard’s famous opening lines (“Now is the winter of our discontent”) before dramatically lurching downstage. Hunchbacked and with a leg brace, he looms over the audience, monstrous against the fast-receding perspective of Tom Piper’s set – a grey chamber with nightmarish, multiple doors.

Spacey’s despot-in-the-making flicks between camp hand-twirls and bullish hollering, and his violently darting seduction of Lady Anne (Annabel Scholey) is almost persuasive. Yet on press night, he ended up rushing and shouting so much that one wondered if half his script was in capitals.

While Richard might be permitted to relish deceptive theatrics, Mendes’s production just looks stagey. Only Chuk Iwuji really shines with a Buckingham of subtle and unexpected nastiness, sleek as a diplomat, with scorn in a faintly cocked eyebrow. Fifteen years ago, Spacey was far better in that role too: a quietly dazzling Buckingham in Al Pacino’s Looking for Richard. But that was then, and this is now.

I guess you could check in for Lullaby instead, if you’d rather get the hump by subjecting yourself to a godawful piece of experimental theatre. Devised by the offbeat troupe Duckie, this immersive show sounds dreamy. It promises a “sublime sleep-over" where you fetch up, with pyjamas and toothbrush, then nestle down at 11pm in a specially created dormitory – nodding off to bedtime stories and rock-a-bye nocturnes. There are single and double beds, and breakfast is served in the morning. What a doss!

The Barbican's studio theatre is, indeed, transformed into a potentially enchanting snuggery, with tiered beds encircling a tiny stage. So Duckie's four performers just needed a modicum of theatrical talent. But they can't sing in tune or read from a book without fluffing their lines, possibly because – judging by the quality of the writing – it's something they scribbled five minutes earlier. Also, why do they keep feebly shuffling around in infantile octopus and whale outfits, as if we're all under five? If it's meant to be ironic kitsch, they're not even any good at that. The show could only benefit from the speedy application of the blindfold and earplugs supplied as slumber accessories.

Perversely, though, I began to find it a hoot, reduced to fits of giggles by Lullaby's unbelievable incompetence; by the thought that I'd made my partner accompany me to this; and by the sight of my fellow critics starting up from their pillows as the performers got a merciless second wind and launched into a garbled lecture on Pythagoras and the music of the spheres. At about 2am, my now bug-eyed beloved mumbled something about "Should have been billed as sleep-deprivation torture" and staggered off to hail a taxi. I downed a large brandy in the foyer (supplied by charming all-night ushers) and tottered back to see if the resounding lone snorer had turned into a chorus.

There was no dozing off at The Beggar's Opera, even though I was swathed in a blanket – it being a chilly evening – and even though Lucy Bailey's al-fresco production has dull patches. Centred on the wenching highwayman Macheath, John Gay's cynical, 18th-century comedy about London lowlife and profiteering is punctuated with lovely folksongs. Yet many are snippets that barely get rolling.

William Dudley's set is entertaining in itself, with wooden carts doubling as giant beds then tipping to form Newgate's prison walls. David Caves' Macheath is mellifluous when he sings and he fondles the swarming floozies with gusto. Still, Phil Daniels is a more amusing rough diamond as the jailer, Lockit.

Disappointingly, though, Bailey has failed to tease much fine acting from her cast and, though the violence and sexual abuse depicted is presumably meant to be more edgy than comic, the tone is too often unclear.

'Richard III' (0844 871 7628) to 11 Sep; 'Lullaby' (020-7638 8891) to 24 July; 'The Beggar's Opera' (0844 826 4242) to 23 July

Next Week:

Claudia Pritchard packs an umbrella for Chichester Festival Theatre's Singin' in the Rain with Adam Cooper

Theatre Choice

Shakespeare's "lost play" Cardenio proves witty and vibrant directed by Gregory Doran, at the Swan in Stratford-upon-Avon to 6 Oct. Dominic Cooke's Royal Court revival of Chicken Soup with Barley, Arnold Wesker's portrait of Jewish East Enders losing their faith in left-wing politics, has been extended to 16 July.