I haven't heard of that. However, Nazi Germany did 'accidentally' bomb London on at least one occasion. Bombers were instructed to bomb a RAF (Royal AirForce) base in August 1940. They drifted off course and bombed London instead, resulting in a number of civilian casualties. I have no primary source handy, but it is mentioned here: http://en.m.wikipedia.org/wiki/The_Blitz
If I remember correctly, Brittain responded by bombing German cities. Will have to look up more info on that later though.
Edit: the accidental bombing of August 24th was in fact the first bombing of London. It escalated the (air-)war and lead to the bombing of many British and German cities.
Your teacher appears to be correct OP, or at least people at the time believed this to be true. See page 7 of this mass-observation summary PDF document
You can read about how mass-observation worked here as well. http://en.wikipedia.org/wiki/Mass-Observation
It's difficult to pin down; London was not specifically targeted until September 7th 1940, but as the Luftwaffe became confident that the RAF were on the brink of defeat in the second half of August, wider military and industrial targets were progressively brought under attack, including targets in London suburbs such as Croydon and Wimbledon (for example Erprobungsgruppe 210 mistakenly attacked Croydon airfield instead of Kenley on August 15th, hitting an adjacent soap factory in the process resulting in 62 civilian casualties).
The first significant attack on London is usually considered to be on the night of August 24th/25th, when Heinkels of KG1 bombed the East End of London; the general consensus is that it was a result of navigational error, and the intended target was either oil terminals at Thameshaven or aircraft factories in Rochester. Some believe it may have been a deliberate attack (e.g. [this page] (http://www.battleofbritain1940.net/0029.html) on the Battle of Britain Historical Society site), but as Goering wanted to transfer those responsible to the infantry (as per Bungay's Most Dangerous Enemy), navigational error is entirely plausible.
There may have been prior instances of bombers jettisoning their payload, but it was the attacks of August 24th/25th, together with the cumulative civilian casualties of Luftwaffe attacks, that prompted the RAF raids on Berlin, which in turn were one of the factors (but not the only one) that caused the Luftwaffe to specifically target London.