The National Theatre today announced details of 2012 productions opening this summer and autumn, including the final show in the current Travelex £12 Tickets season and a packed festival programme of outdoor events to celebrate the Jubilee and London 2012 Games.

Fiona Shaw leads the cast in a new production of Howard Barker's Scenes from an Execution. Directed by Tom Cairns, with a design by Hildegard Bechtler and sound and music by Ben and Max Ringham, the play previews from 27 September at the Lyttelton.

Scenes from an Execution is set in 16th-century Venice, where free-spirited painter Galactia – played by Shaw – is commissioned to paint an enormous work celebrating the Battle of Lepanto, in which Venice triumphed over the Ottoman Empire. More concerned with serving the truth than her patrons, Galactia falls into disfavour and must relinquish the commission to her young lover, Carpeta.

This dark, irreverent piece about the shadowy territory between personal ambition and moral responsibility was first written for radio before being adapted for the stage in the eighties. It is the first time a work by Barker, a playwright and dramatist far better known in Europe than at home for his provocative, European-influenced theatre practice, will be staged at the National. Director Tom Cairns returns to the theatre for the first time since his NT debut with Aristocrats in 2005.

Meanwhile in the Olivier, Olivier Award-winning Bertie Carvel will play Enrico to Sebastian Armesto's hermit Paulo in the 1635 Baroque drama Damned by Despair. As previously reported, NT associate director Bijan Sheibani directs Frank McGuinness's new version of Tirso de Molina's play about faith, redemption and love.

The final production in the Travelex £12 Tickets season, Damned by Despair opens on 2 October and runs in repertoire thereafter. It features set design by Giles Cadle. The cast includes Rory Keenan and Amanda Lawrence.

Carvel received the 2012 Olivier Award for Best Actor in a musical for the role of Miss Trunchbull in the RSC's Matilda the Musical. He will play his final performance as Miss Trunchbull on 1 July.

As previously announced, This House, a new play by James Graham, will open in the Cottesloe on 18 September and run in repertoire until 1 December. Directed by Jeremy Herrin, the play is set in Westminster in 1974, at a time when the UK was facing a hung parliament and economic crisis. The cast includes Phil Daniels, Philip Glenister and Julian Wadham.

National Theatre Inside Out

Between June and September the National's public and outdoor spaces will be home to a series of events, many of them free and participatory.

It all kicks off on 1 June with the Watch This Space festival, which returns to Theatre Square for a 14th year of international circus, street performance, dance and more. The free festival runs all summer and includes performances from renowned aerial company, Ockham's Razor.

Taking place on the Riverside Terrace from 2 June will be The Pop-Up Workshop, in which prominent theatre-makers, including playwrights, puppeteers and costume designers, will lead public workshops. Many events are free but most require advance booking in this series designed to showcase the inner workings of the National. 

In another first, two site-specific commissions from companies affiliated with the NT Studio will be transforming secret rooftop locations into theatre spaces as part of the London 2012 Festival. Get Stuff Break Free runs from 25 June to 4 July and you'll see me (sailing in antarctica) runs from 6 to 15 July.