The hour-long show peaked at 5.1m as viewers tuned in to see a mix of drama and archive footage of how 338,000 men from the British Expedition Force, along with French comrades, were rescued from the beaches of France in the early summer of 1940 in what the Royal Navy called Operation Dynamo.
Peter Paterson in the Daily Mail described last night's opening instalment as "excellent" and praised the powerful performances of Simon Russell Beale who became the latest actor to portray Winston Churhill.
Russell Beale's portrayal had Churchill riding roughshod over colleagues and appeasers in the dramatised meeting of the wartime British cabinet. In one extract, Churchill tells Lord Halifax "it would be no bad thing to go down fighting".
In the Daily Telegraph John Keegan said he was struck by how "fair a picture of that extraordinary episode it conveys", and how "accurate the history is, and how well judged is the script as drama".
There had been fears that the BBC story of 'Dunkirk' would fashionably debunk history but Keegan said he found none of that. "The BBC has been under attack recently. It deserves praise for the intellectual integrity and inspiration of its Dunkirk series."
The programme gave not only the stories of the cabinet but the ordinary soldiers, sailors and civilians caught up in the events and the desperate race to save British troops trapped in France.
During the making of the programme the BBC team interviewed more than a hundred survivors who shared their memories and experiences with the programme makers.
Neil McKay, co-writer of 'Dunkirk', said: "One of the reasons why it seemed so important to make the drama now is that the survivors of Dunkirk are in their eighties or older. In 10 or 15 years the people who went through this extraordinary experience may be gone and the opportunity will have been lost for ever."
He added: "We hope the films will not just be gripping drama, but a fitting tribute to those who went through the experience of Dunkirk."
If the British had failed at Dunkirk almost the entire British Expeditionary Force in France would have been captured or killed. Initially it was thought that only 45,000 of the soldiers trapped on the beaches could be rescued, but 10 days later more than 300,000 had been brought home, the bulk of the troops crossing the channel in Royal and Merchant Navy ships.
All the characters in the BBC programme are real and all the events are taken from these first-hand accounts. 'Dunkirk' is being shown over three successive nights at 9.00pm starting with the second episode tonight.
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