Anyone interested in maps and London could do far worse than visit Mapping London, a fascinating website created by people with far more technical skills than I could hope for. One really interesting map that shows the diversity of London very well is a map of London by most common surnames. Browsing the map you can see how the residents of different areas have strinkingly different heritages - the map includes colour coding to show the origin of that surname.
When I moved to the East End I was amazed by how many 'Begum's there are, and clearly it is a very common surname, but it strikes me how rigidly its occurence sticks to borough boundaries. It would be fascinating to see a dynamic map showing this data over time. Until then I think we'll have to wait and see.