Armstrong's theatre work includes Flare Path (West End) and The Empire (Royal Court), while Wood has recently been seen in King Lear and Filumena at the Almeida, as well as Flare Path.
The two-hander is set in an airless, windowless basement, where two hit men await their orders. The last job has got Gus thinking while Ben just wants a cup of tea. But their usual routine is disturbed and events start looking ominous when the unexpected and increasingly perplexing messages start arriving through the 'dumb waiter'.
The production runs at the Print Room from 23 October to 23 November.
The 1970 drama is billed as a "beautiful, compassionate, tragic and darkly funny study of the human mind and a once-great nation coming to terms with its new place in the world".
The production marks the return of Alex Waldmann's company SEArED to the Arcola following its revival of Dennis Potter's Brimstone and Treacle last year.
The play, which runs in the main space Park200, is set on US election night in 2008 and examines multiculturalism in a smart inner-London 'village'.