Fact

• London: The Biography by Peter Ackroyd. One of the best books about dear old Londinium ever. It's not chronological - it's based on themes such as sewage, food, childhood and poverty and is immensely readable.
• The London A-Z. Invaluable if you're a London or visitor - I never leave the house without one. You can find out a bit about the history of the company behind it at a-z maps. Artist Phyllis Pearsal (1906-1996) worked 18 hours a day walking the streets, designing and producing the first map. She also formed her own company to produce it - you'll find a detailed article about her at Design Museum.
• London: A Social History, by the sorely missed and extremely well-regarded historian Roy Porter. This is another readable history of London and its people by an author who ...moved easily between social, medical and psychiatric history, and was never better than when describing eccentricity and extremes of temperament.

Fiction

A longer list of books set in London (in no particular order);

• Three Men in a Boat (To say nothing of the dog) See The Jerome K Jerome Society for the story behind this classic.
• Another comic everyman story set in Brickfield Terrace, Holloway abode of Charles Pooter, Diary of a Nobody. Charles even has his own Myspace profile. Author George Grossmith.
• The Drowned World by J G Ballard introduces us a London of lagoons, where iguanas inhabit the empty boardrooms. Not a man-made global warming, this heat is caused by something much more plausible - the sun and the earth's proximity to it.
• Robert Rankin has written more than a few books (with his own inimitable sense of humour) based in London and its environs in the comedy/fantasy genre - these include classics such as The Brentford Triangle and The Witches of Chiswick
• Neverwhere by Neil Gaiman. One of the best fantasy books I've read in years. This features a whole other world under the London earth with characters such as the Angel Islington and the Blackfriars, never mind an Earl's Court travelling around in a tube train.