It was a moment when the nation’s very survival lay in the balance — three days in May 1940 during which Winston Churchill and his war cabinet agonised over whether to talk terms with Adolf Hitler (in effect, give in to him, as our new Prime Minister clear-sightedly realised) or stand alone, very nearly, against the Nazi aggressors. This is the period of high political drama studied in Ben Brown’s gripping new play, Three Days in May.

Of course, we know the decision that was reached — one of momentous importance for Europe and the world. But this makes seeing how it was reached no less compelling. The remarkable thing is that no one knew how close to the abyss the country had stood until decades later. That submission had even been considered was unknown until wartime papers were released under the 30-year rule.

The play begins — following a scene-setting introduction by Churchill’s private secretary, Jock Colville (James Alper) — with a tense two-man Downing Street summit. The nation’s new leader, appointed two weeks earlier, is told by the French president Paul Reynaud (Timothy Kightley) that his battered forces can fight no more. Mussolini is offering to help broker a peace with Hitler. The offer is being accepted. It is hoped that Britain — with its own Expeditionary Force preparing to flee Dunkirk — will share in the bid for peace.

The matter is laid before the five-strong war cabinet whose discussions, over three crucial meetings, form the principal ‘meat’ of the drama, with the action confined almost totally to No 10 Downing Street, its cabinet office atmospherically presented — a huge map of the world covering one wall — in Gary McCann’s design.

The house remained at that time home to the recently deposed Prime Minister Neville Chamberlain (Robert Demeger), still the leader of the Conservative party and a man of considerable political clout. Despite the bitter experience of Munich behind him, he at first shares the view of the icily patrician Foreign Secretary Lord Halifax (Jeremy Clyde) that it remains possible to talk peace with Hitler. The Labour members of the cabinet, by contrast — party leader Clement Attlee (Michael Sheldon) and his deputy Arthur Greenwood (Dicken Ashworth) — are minded, like Churchill, to fight on. Greenwood argues powerfully that the British public would not tolerate surrender, which suggests that his name deserves to be more honoured in the annals of the period than it generally is.

What Churchill seeks is a unanimous voice from his coalition cabinet, and how this is achieved — by means of informal meetings, separately, with his two opponents — show the great man to have been as persuasively eloquent, and as cunning, in private as in his public performances.

This is obviously a play that makes heavy demands of the actor playing Churchill, whose gruff, slightly lisping voice, whose looks and whose body language — think that cigar! — are familiar to all. Warren Clarke rises to the challenge brilliantly, showing us Winston’s warmth and humour in private — his fatherly regard for young Jock Colville is especially affecting — and the forceful grandiloquence of the public man. The one famous speech (building towards “It is better to perish than to live as slaves”) is superbly done. Clarke’s one minor failing, which he shares with the Simon Ward of Young Winston, is to pronounce ‘circumstances’ to rhyme with ‘chances’, something few upper-crust chaps of the time, and certainly not Churchill, would have done.

Three Days in May continues until Saturday. Booking: 0844 871 7652 or www.ambassadortickets.com/miltonkeynes. The play is at London’s Trafalgar Studios from October 31 until March 3, 2012.