British historians generally accept July 10, 1940 as the start of the Battle of Britain. German historians don't have it starting until after the initial phase the British call the start. The Germans called the initial phase the Kanalkampf, the Channel battles. A series of running air battles erupted over convoys and shipping in the English Channel, lasting through August 11, 1940 when the Luftwaffe switched from shipping to attacking airfields.
The British, despite using obsolete tactics and having a severely limited supply of qualified fighter pilots managed to hang on and defeat the Germans in the skies over Britain. When it was all said and done, Winston Churchill summed it up with one of the most famous lines he ever spoke:
"Never in the field of human conflict was so much owed by so many to so few."
(More excerpts from that speech can be found here. The British Battle of Britain historical website features the actual command diaries that Fighter Command kept throughout the battles. There is also an official historical society with a number of resources.)
Been to those sites. B of B as interested me since I was a young boy.
I read a quotation somewhere from an RAF officer, who said of the “Never… was so much owed by so many to so few” line, “He must have been talking about our bar bill.”