The rhyme was first recorded in 1744, with some slight variations. The refrain 'My fair lady' was written as 'with a gay lady', and London Bridge wasn't 'falling down', it was 'broken down'.

The couplets are considered to be a dialogue between two people, and were recorded around 1825 as:

Build it up with wood and clay
Wood and clay will wash away
Build it up with bricks and mortar
Bricks and mortar will not stay
Build it up with iron and steel
Iron and steel will bend and bow
Build it up with silver and gold
Silver and gold will be stolen away
Set a man to watch all night
Suppose the man should fall asleep
Give him a pipe to sleep all night

It is possible that the couplets used to rhyme. Iron and steel will bend and yield, silver and gold will be stoled, and, this Researcher suggests, bricks and mortar, do we oughta? As the language of the people singing the rhymes change, so do the nursery rhymes.