Things are in a bad way when Churchill takes over as prime minister. France's defences have crumbled and, as the Germans are advancing, the Allied forces- predominately British- are being forced to retreat to the beaches of Dunkirk and Calais where, boxed in, they are literally caught between the devil and the deep blue sea. Britain is facing the probable loss, in casualties and POWs, of over 300,000 men.
The rest is, as they say, history. Operation Dynamo, which saw civilian boat owners mobilise to cross the Channel and rescue the trapped soldiers was a miraculous success, with over 338,000 men evacuated. Britain lived to fight another day, and fight they did under the leadership of Prime Minister Winston Churchill.