It's time to grapple with the biggest misconception about London: that it's one city. Actually, it's two separate cities, with one completely surrounded by the other. The city surrounded on all sides is the City of London (also known as the Square Mile or simply "the City"), and the city doing the surrounding is, well, London. Let's not get started on whether Greater London is really called Outer London... The above video explains it all very thoroughly (and is funny too).