It’s likely that this rhyme commemorates the joining of Scotland and England in 1603. The Lion and the Unicorn came about when James VI of Scotland became James I of England.
The royal coat of arms of Scotland bore two unicorns. Today, both the lion and the unicorn are symbols of the United Kingdom, the two animals being featured prominently on the coat of arms.
The Lion and the Unicorn Lyrics
The Lion and the Unicorn were fighting for the crown;
The Lion beat the Unicorn all round about the town
Some gave them white bread, some gave them brown;
Some gave them plum cake, the drummed them out