London Bridge did fall down - several times in fact. And just as the famous nursery song implies, it has been rebuilt and rebuilt using various materials.
A bridge was present at or close the present London Bridge some 2000 years back. The oldest version was wooden and built by Romans around 60 A.D. This bridge fell sometime after they left. It was believed to have been rebuilt using timber several times after that. The bridge had another mishap when King Aethelred burned it down in 1013. It was renovated, but was again destroyed in a 1091 storm, and furthermore by an 1136 fire.
After its 1136 fire accident, Peter de Colechurch, London Bridge's maintainer proposed to change the bridge's timber material using stone construction. The stone version was completed in 33 years, around 1209. King John, who reigned during this time, allowed people to put up houses and shops on the bridge. Numerous structures took up most of the bridge's space. Because of this, it wouldn't be surprising why the London Bridge faced a lot of disasters. Several more tragedies occurred until the end of the17th century.
Towards the last part of the eighteenth century, the London Bridge showed signs of needing repair. A new bridge was then built in 1824 and was completed in 1831. The old bridge was continually used while the new one was ongoing construction, but was demolished during the project's completion in 1831.
The London Bridge was sold and reconstructed. It was disassembled and reconstruction was done in Lake Havasu in Arizona. Next to the Grand Canyon, the London Bridge became the second most popular tourist spot in Arizona. Not every piece of the London Bridge left London. The remaining 'pieces' were kept at Merrivale Quarry in Devon. When the 2003 flood hit Merrivale, some pieces of the bridge were auctioned online.
The present London Bridge was opened on March 17, 1973 by Queen Elizabeth II. It was built in the exact location of the previous bridge before it was brought to Arizona.
Disaster struck the bridge again in 1984 when a British warship collided with it. During the 2004 Remembrance Day, red lights were placed on the different bridges of London. It has improved London Bridge's dull appearance that's why the red lights were not removed even after the celebration.
With the very rich history of the London Bridge, no one would dare wonder why it has inspired the creation of a nursery song.