I cannot see why Heathrow is precluded because it is in a built up area.
Its not precluded. It is however undesireable and as per the AAIB report on N481EV provided by WHBM earlier here, if the Safety recomendations, have been implemented, then since the crew had already declared a PAN, ATC would be required to either come up with a routing that doesn't fly over a densly populated area (just a little hard here) or suggest alternative aerodromes... From the report:
10.10.2 It is desirable that aircraft in emergency should not be routed over densely populated areas. If this is inconsistent with providing the most appropriate service to the aircraft, for example when any extended routeing could jeopardise the safety of the aircraft, the most expeditious route is the one which should be given. Where possible, when expeditious routing is not required, suggestions of alternative runways or aerodromes together with the rationale that the routing would avoid densely populated areas and be consistent with safety, shall be passed to the pilot and his intentions requested.
It would be good to understand if ATC did offer the appropriate advice, and if they did, why the crew rejected the advice and continued to Heathrow.