Yes and no. As always, the situation was never that simple.
While Hitler had used aerial bombardment against civilian populations in the 1930s to help force capitulation from some European governments, he was worried about retaliation from Britain against the German population and so was reluctant to begin a broad bombing campaign on the British population. However, Hitler actually had little direct control over the Luftwaffe by August 1940. Göring had successfully gained independent control - and was very clever at misrepresenting reports to keep his independence.
Still, during the initial phase of the Battle of Britain, the Luftwaffe mostly targeted shipping, RAF radar and airfields, and plane factories, in an attempt to break the RAF defence and gain the vital air superiority over the Channel which would be necessary to launch an invasion.
The first bombs on London fell on August 24th. This was probably an accident due to lost pilots. Britain did send bombers to Berlin the next day.
Now, works like The Battle of Britain (which is an excellent movie, and gets most of the history right with some artistic licence) would have you believe that is where it started. Hitler gave a rousing speech and promised "moar bombs" in return for what the RAF dropped on Berlin.
But it was actually two weeks later that the Blitz really started. The Luftwaffe continued pressing their attacks on the RAF and factories until September 7th when Göring and his command (under pressure from a frustrated Hitler) acted on intelligence that brought them to believe the RAF was at breaking point, and the Blitz was seen as the final phase of annihilation before the sea invasion.
So - while London was probably bombed by accident on August 24th - it was not the primary cause of the Blitz.