I agree that Britain did not quite "stand alone" after the defeat in France. Members of the Commonwealth had made their own independent declarations of war on Germany. India as part of the Empire declared war in 1939. Nepal for example was at war and was not a member of the Commonwealth. Thousands of Irish moved to Britain to fight.
Even though France, Poland and Czechoslovakia were defeated, thousands of their soldiers, including those evacuated from Dunkirk fought with the along side the British and as members of the RAF. De Gaulle was leading the Free French forces.
However, Britain was the only country in Europe that was at war with Germany and had not surrendered. In that sense, she was proudly standing alone.