Del Prado
Should aircraft in an emergency be vectored clear of built up areas?
Usually ATC will ask if there are any problems maintaining height or control of the aircraft. If not, then no need to avoid any built up areas.
If there are problems maintaining height or control, then avoiding built up areas, although a concern, isn't going to be easy since the aircraft won't be doing what the pilots want it to do anyway.
If the problem is serious enough, they probably wouldn't be going to a London airport anyway but the nearest suitable runway.
So the answer to your question, like I said before, is no.
And I would hazard a guess that the answer to:
Who's responsible for avoiding built up areas? (and where is the guidance?)
..would be the commander of the aircraft I suppose.