I'm not sure how plausible this is, but here goes.
I read in "The Century" that the London Blitz of 1940 only started when a German bomber accidentally dropped a bomb downtown instead of on the military target it was aiming for. Churchill hit Berlin in response, and everything escalated from there.
Suppose there are no errant bombs. Are the civilian sectors of London still attacked? If not, how would the hesitation of attacking civilians play out during the rest of the war?
The Germans weren't trying to hit a military target, they were trying to hit an industrial target - which happened to be the Thameshaven oil terminal, very close to wide built-up areas of London. They tried this at night, in the full knowledge that their targeting was not good enough at night to guarantee they wouldn't bomb the city. Nor did they send enough bombers on this mission to actually cripple the terminal, if they had hit it.
In other words, the Germans were making up a poor excuse. The purpose of the mission was to frighten British civilians, Londoners, by having the sirens wake up them at night - without, however, actually and openly targeting the city. It was a practice the Luftwaffe had learned and applied before; choose a legimate military or industrial target, but make sure it also hurts either the civilians' morale or the actual civilian buildings.
As it was wont to happen, the German bombers peppered the city. Luftwaffe fanboys will tell you that the wily British used this opportunity to shift the focus to city bombing, and maybe that this is the reason why the Luftwaffe was soundly beaten in the Battle of Britain.
Actually, it was already clear the Germans could not win in the daylight air battle. They couldn't keep up with their own losses. The strategy of attacking the airfields wasn't producing the desired result.
And, it was only a matter of obvious political expediency that once the enemy bombs your capital, if you can, you'll bomb the enemy's capital. The actual words of Churchill to the Air Staff were: "Now that they have begun to molest the capital, I want you to hit them hard, and Berlin is the place to hit them".
There's more. If we swallow the line that the city bombing tit for tat developed either by mistake or by a mistake compounded by the supremely cunning British riposte, all of that could well have remained a night campaign. Instead we had the September 15 daylight attack. Why?
Because the ban on bombing London had been lifted, and Kesselring was very much aware he wasn't achieving victory. Dowding was committing his fighters conservatively; the British fighters were regularly outnumbered by the forces they were sent to attack, yet they managed to give more than they took. At the same time, the Germans weren't destroying any operational fighters on the ground, nor were they damaging the airfields permanently and enough to really hamper operations.
The Germans thought they had to destroy Fighter Command in the air, but they couldn't do that if the British fighters only arrived in small numbers and piecemeal. They wanted a big battle, the Götterdämmerung of Fighter Command.
The Germans thus put their hopes in a last-gasp maximum effort over London. They thought the British would be forced to send all their few (?!) remaining fighters to defend the capital, and that they would be destroyed.
Final tally for the day: 56-28, a neat 2:1 kill ratio in favor of the British.