Here is a recording of the appeal made four days later, on the 22nd. On the 18th the BBC didn't record the speech. However the word spread in France after 18th and on the 22nd many more listened. And on the 28th Churchill's government recognized De Gaulle as 'leader of all the Free French'. 'This was vital, but it laid him open to accusations of being a British puppet, ' write Robert and Isabelle Tombs in their brilliant book on Anglo-French relations, 'That Sweet Enemy' ('Cette Exquise Ennemie'). Not only few heard, initially, even fewer joined the General.
"Is defeat final? No! De Gaulle was saying.
"Believe me, I who am speaking to you with full knowledge of the facts, and who tell you that nothing is lost for France. The same means that overcame us can bring us victory one day. For France is not alone! She is not alone! She is not alone! She has a vast Empire behind her. She can align with the British Empire that holds the sea and continues the fight. She can, like England, use without limit the immense industry of the United States."
'Petain's authority and ambient Anglophobia blighted de Gaulle's efforts to rally support. ... Those who did join de Gaulle were not only adventurous, but junior and often rather unusual... This gave the Free French a reputation for extremism and eccentricity. De Gaulle was no more successful among permanent French residents in London, of whom there were about 10,000: only 300 volunteered. Civilian refugees, like those in uniform, mostly wanted to get home.'(from 'That Sweet Enemy')
Full text of the appeal is here in English and here in French.
On the same day Churchill spoke in Parliament of the coming 'Battle of Britain'. It is that speech which is remembered by the rousing words, in a thousand years, men will still say: 'This was their finest hour.'
President Sarkozy is in France today for commemorations of l'Appel de 18 juin: