A discussion and particular reference to this incident was included in a good deal of a recent thread in which a number of us where considering the possible outcomes of the war if Britain had been invaded after Germany had won the BoB.
(Don't recall the thread, but it was pretty recent - maybe someone can direct us?).
Anyway, with regard to the incident, I have seen a couple of Doco's and read the odd account, and it would seem that a "single" He111 crew did get lost on the date mentioned (my info isthe evening of the 23rd August). The aircraft commander (pilot) panicked and ditched his bombs ACCIDENTALLY over London.
The British should have realised that a single plane load of bombs dropped on an insignificant part of London (although not insignificant to the people who lived there), did not constitute a "raid" as such and was probably a mistake.
But for whatever reason, the British retaliated with a "purposeful" raid on Berlin ("You can call me Herman")

and Hitler got so incensed that he directed the Luftwaffe to change there targetting to English cities, especially London.
This took the pressure off Fighter Command who had been suffering daily attacks on airfields and factories and yes, they were on their "last legs".
Incidentally, Oz, the Germans never really considered the "Chain Holme" system a viable or necessary target. They did attack with JU87's in reasonable force on one occasion, and there were a couple of further "half hearted" attempts, but very little damage was ever done to the system. it always worked well enough to serve it's purpose and (to my knowledge) was never in danger of collapse.
However, as you point out, the RAF were in very serious danger of collapse and this one single incident did (albeit unintentionally) change the focus of the battle to bombing of the cities rather than destruction of the RAF.
Apparently Hitler (and maybe others) considered it possible to "demoralise" the British to the point of suing for peace. This, at least, is a common view among historians when asked about the "ineffective" nature of this bombing of cities of no real strategic military value.
Incidentally, given the climate in Germany and the manner with which Hitler and his mob dealt with failure and negligence, you might be forgiven for thinking that the responsible crew were shot (or something similar).
I have heard that they all actually survived the war. Primarily because they were never allowed near an aircraft again