Although the crew of an aircraft with a problem will have first call on routes etc., in the absence of any preference guidance to UK controllers is:
It is desirable that aircraft in an emergency should not be routed over densely populated areas, particularly if there is reason to believe that the aircraft’s ability to remain in controlled flight is compromised or that parts of the aircraft could detach in flight. If this is inconsistent with providing the most appropriate service to the aircraft, for example when any extended routeing could further jeopardise the safety of the aircraft, the most expeditious route is the one that should be given. Where possible,
when expeditious routeing is not required, suggestions of alternative runways or aerodromes together with the rationale that the routeing would avoid densely populated areas and be consistent with safety, shall be passed to the pilot and his intentions requested.
It is recognised that controllers providing en route services at ACCs may not be aware of the boundaries of major cities, towns or villages. However, controllers providing aerodrome, approach or approach radar control services should be familiar with the centres of population within their areas of jurisdiction.
Controllers should be aware that aircraft experiencing engine failure may also
experience associated handling difficulties and should therefore limit manoeuvring instructions to the minimum necessary.
As I recall, this guidance came about after an AAIB recommendation where an aircraft with severe problems (perhaps only evident after the flight was completed) was vectored over central London.
Important note - I do not seek to suggest that this has any relevance to today's events.