Is the London Bridge the longest bridge in the world?

No. Arguably the longest bridge is the Bang Na Expressway, in Bangkok, Thailand. It is 33.5 miles long (54 km), but is not considered a bridge because it does not cross a single body of water, instead crossing a river and canals.
The longest bridge running over a single body of water in the world is now the Jiaozhou Bay Bridge in China. 42km in length, it links China's eastern port city of Qingdao to the island of Huangdao. The bridge cost over $1.4 billion to build and was completed in mid-2011.