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A 2002 Telegraph article reports:

The first German bombing of London on the night of Aug 24, 1940, was an accident but sparked a war of attrition that would last for five years.

German aircraft heading for a military target flew off course and mistakenly dropped their bombs on central London.

The raid was interpreted by Winston Churchill as deliberate and the following night 40 British bombers were sent on their first attack to the German capital Berlin.

A June 2018 War History Online also makes the claim:

By most accounts the bombing on August 24 was an accident. German bombers, that were supposed to hit military targets outside of London, flew past and struck part of the capital itself, causing some damage and civilian deaths.

I found the claim first in this Quora answer

That changed in September 1940 when London was accidentally bombed by a small number of German bombers who were off course and bombed London by mistake. The British retaliated by spending a small number of bombers to Berlin. After that, the gloves came off and Germany targeted London and other British cities.

These sites to do not list sources.

There's no mention of it in the Wikipedia article on The Blitz, but under the entry for August 24th on page for August 1940 is says:

The Luftwaffe dropped bombs on the financial heart of London and Oxford Street in the West End, probably unintentionally as the German bomber pilots had likely made a navigational error and did not know they were over the city.

The three provided references are: a book I can't access, a dead BBC link and link to a Battle of Britain history website that doesn't mention it under the August 24th entry.

Yes, we have a number of reasons for believing the idea that it was an accident, based on Luftwaffe bombing patterns, the raid itself, and Hermann Göring's orders.

The Luftwaffe was not trying to destroy London.

Since the middle of 1940, the Luftwaffe had been trying to destroy the Royal Air Force, in preparating for the planned Operation Sea Lion, to conquer Britain. As such, many of the targets were RAF airfields, as well as industrial facilities:

The campaign launched in the summer of 1940 was designed to prepare the ground for the planned invasion of Britain, Operation Sea Lion, authorized by Hitler on 16 July 1940. This was to be essentially a form of longrange tactical bombing against RAF and military targets to eliminate British air defences and offensive capability.

In Fighter Boys, historian Patrick Bishop writes (page 296)

On 25 August the weight of the attacks shifted to the south and west and attacks were launched on Portland, Weymouth and Warmwell airfield in Dorset. . . On the morning of 26 August the attacks swung back to the 11 Group airfields, with a formation of forty Heinkels and twelve Dorniers making for Biggin Hill.

Bishop's point is that the attack on London was an anomaly. The Luftwaffe continued, for several weeks, to continue bombarding its old targets: airfields and industrial facilities. Moreover, the targets were not near London, merely Group 11 airfields (southeast England and the approach to London).

This was a small-scale bombing raid and poorly concentrated.

To bomb London would have been a massive shift in German strategy, and likely would not have involved merely two bombers. However, the bombs that fell that night fell in two clusters, one of which wasn't even close to London, originating from two different airplanes.

The sustained attack on London didn't begin until September 7th. This was a series of deliberate raids that involved nearly continuous daily/nightly bombing for almost two months. After a switch to nightly raids, the Luftwaffe bombed London for 76 consecutive nights. In short, if the August 24th/25th raid had been intentional, it would have been extremely uncharacteristic of the Luftwaffe's strategy during this time period.

Nothing suggests that Göring ordered it.

We know that, as of the middle of August of 1940, Germany was prepared to possible bomb London and other major British cities, in addition to their industrial and military (essentially, non-civilian) targets. However, going into August 24th/25th (including the raid that included the first bombing of central London), there was no intention to do so just yet. On August 19th, Hermann Göring issued a document stating

There can no longer be any restriction on the choice of targets. To myself I reserve only the right to order attacks on London and Liverpool.

The thing is, we have nothing to suggest that Göring gave that order several days later. Many Luftwaffe documents from the night of August 24th/25th are missing, but any command to bomb London would likely have been well-documented.

Bishop also writes (page 295) that Göring was in fact displeased by the result of the raid, though no German primary sources are specifically cited for those remarks:

The breach of orders was blamed on an error in navigation. Goering, anticipating a storm of rage when Hitler heard the news, demanded to know who was responsible and threatened the guilty with a transfer to the infantry.