I don't think stating as your intentions "I want to circle around a bit to look at the pretty houses" will get you anywhere with your average air traffic controller,
I don't see any reason why not.
Air traffic controllers are there to help the pilot, not the other way round, or so I have been told by Air traffic controllers I have spoken to.
They may say "No we are too busy" but they (shouldn't) just say no for the sake of it, even in Hallowed London.