CM...
Flying "low over London" to reach LHR, or not, does come under common sense, and to knowingly hazard the City by flying an airliner with a distinct possibility of "coming down" could be seen as unwise. See the 747 with potentially no engines report.
However, I am not sure that Rule 5, which does (IMHO) apply as much to us as a light aircraft, is relevant here.
You have subtely altered things as well, going from
because I chose to divert to a rural airport rather than go into LHR with a problem necessitating an engine shutdown at TOD (leaving me single-engine).
to
is that it is NOT necessary to fly past a serviceable, fairweather, suitable airfield and continue single-engine to fly over the city at low altitude.
I would agree - in Airbus speak single engine is Land ASAP - and "pressing on" to LHR might need justifying - whereas your first post implied you actively sought an airfield that was "not LHR".
In short, an interesting debate. However, I am not convinced that LHR/London is a "special case" - very few airports we fly into are truly remote, and under the ANO definition (2000 people?) airports and the associated infrastructures are towns in themselves... and the weather's we train to fly in are not sufficient to meet the Rule 5 requirements i.e. guarantee being able to force land without danger to persons or property (NB this does not say minimise - it as bad a breach to hazard 1 person and his bicycle as the whole of the City <G> )