13, NT Olivier, London / Marat/Sade, Royal Shakespeare Theatre, Stratford-Upon-Avon / The Last of the Duchess Hampstead

Talking about a revolution: that’s what the NT and the RSC were both up to this week. Each was tapping into the zeitgeist with more pessimistic gloom than real incendiary zeal, however.

Set in a fictionalised modern-day London, Mike Bartlett’s new National Theatre drama is portentously titled 13. And the capital’s inhabitants – from the Conservative PM to your man in the street – keep having the same recurrent bad dream, featuring monsters and explosions. Yeah, it’s ominous.

In Thea Sharrock’s production (with set design by Tom Scutt), a black tower spins into view, accompaniedby menacing rumbles. Behind its multi-storey windows, the city’s troubled souls are glimpsed twitching in their sleep. Then the lights snap up and numerous characters’ lives start criss-crossing.

Protesters are clashing with the police in demos against university fees. We gather the Arab Spring has sprung too, but Britain and the US are on the brink of declaring war on Iran.Suddenly an unkempt young man named John (Trystan Gravelle) emerges from the crowd, a messianic revolutionary.

John starts soap-box preaching about how people should resist warmongering politicians and trust new technology to free the oppressed. He accrues an online following and inspires mass gatherings in Trafalgar Square. The Prime Minister – Geraldine James’s Ruth, in a chic blue suit – summons John to Downing Street.

Bartlett certainly taps into collective anxieties and embraces big issues, as in his previous hit, the apocalyptic environmental drama Earthquakes in London. Yet 13 disappoints. Gravelle’s grandstanding as the dishevelled John, even on a spectacularly rising rostrum, is blandly platitudinous: “We will have standards … things like kindness, politeness, welfare, equality.” This is dull, not dangerous talk.

Most of Sharrock’s ensemble are excellent, including Adam James asafraught lawyer and Danny Webb as a fired-up lecturer. Geraldine James’s steely Ruth is surprisingly persuasive too. But this fluent production can’t conceal garbled subplots. The playwright has clearly bitten off more than he can chew, with racism, sexual politics, Christianity versus atheism and – did I mention? – a deranged infanticide thrown into the mix.

Meanwhile, the Royal Shakespeare Company is reviving Marat/Sade,Peter Weiss’s famed avant-garde take on the assassination of Jean-Paul Marat – the French Revolutionary stabbed in his bathtub by Charlotte Corday. Marat/Sade caused a sensation back in 1964 when Peter Brook staged its RSC premiere. Liberty and censorship were, of course, hot topics then. Weiss also created layers of complexity by making Marat’s 1793 assassination a play-within-a-play, supposedly being staged in an asylum in 1808, under Napoleon’s regime. Thus, wayward maniacs play Marat and Corday under the cynical direction of their fellow inmate the Marquis de Sade, as a wary governor watches.

Weiss’s aim was to mesh Brecht’s alienation techniques with the savagery of Artaud’s Theatre of Cruelty. Alas, the result in Anthony Neilson’s modern-dress production is a conceptual muddle. Jasper Britton’s Sade is dressed like a City banker then a burlesque drag act, while Marat’s nasty parents prowl around in burkas. The Daily Mail has shrieked about Neilson’s outrageous sex scenes, but really they’re a puerile bore – unconvincing lunatics brandishing rubber dildos. Nobody stormed out on the night I attended. The final question put to Sade, “Has this drama in our bath hall/ Eluci dated anything at all?” raised a weary laugh.

For The Last of the Duchess we’re in a Paris mansion, but it’s 1980 and Wallis Simpson won’t be guillotined inNicholas Wright’s new play, based on Lady Caroline Blackwood’s biography of the same title. Besides causing the abdication of Edward VIII, Simpson was suspected of Nazi sympathies, but in this slightly staid chamber piece we see her as an ailing widow, fiercely protected by attorney Maître Suzanne Blum (Sheila Hancock, amusingly snappy).

For sequestering the Duchess and spin-doctoring, it seems Blum may be subjectedto a hatchet job by the riled Lady Caroline (Anna Chancellor) who becomes woven into her own narrative. This seems an odd decision on Wright’s part, for in questioning Blackwood’s objectivity, he implicitly questions his own.

‘13’ (020-7452 3000) to 8 Jan; ‘Marat/ Sade’ (0844 800 1110) to 5 Nov; ‘The Last of the Duchess’ (020-7722 9301) to 26 Nov