I was born in London and moved straight back here after I graduated. I know the city extremely well, so I'm going to make my reply about books based in London. So, off the top of my head:
One of my favourite books is the Pulitzer winning Foreign Affairs
I have a vast collection of crime fiction, much of which uses London almost as a character in its own right. In particular, I'm thinking of Ruth Rendell's The Keys to the Street, which is set in and around Regents Park, and PD James' poet detective Adam Dalgliesh who lives on the river in Rotherhithe. In Original Sinhe investigates a murder in a publishing house on the banks of the Thames, and in The Murder Room the crime takes place in a museum on Hampstead Heath.
My absolute favourite piece of period crime fiction is Margery Allingham's The Tiger in the Smoke
The make-up of the population of London changed dramatically through the 20th century to the present day. Two books that look at the fabulously diverse nature of our city are Brick Lane
I don't think you can understand London without reading about the Second World War which changed the city in such a physical and emotional manner. RF Delderfield's cracking good reads, following the fortunes of the Carver family and their neighbours, are a good start. The Dreaming Suburb
The Night Watch
I'm sure my erudite readers have many more suggestions: do leave them in the comments box below, as I know we'd all like some additions to our reading lists.