does it has adapted into any game?
Yes, the rhyme is often used in a children's singing game, which exists in a wide variety of forms, with additional verses.
London Bridge Is Falling Down
The rhyme is often used in a children's singing game, which exists in a wide variety of forms, with additional verses. Most versions are similar to the actions used in the rhyme "Oranges and Lemons". 
where did the song london bridge is falling down come from England
wiki:7427107
London Bridge Is Falling Down [SEP] The game
The rhyme is often used in a children's singing game, which exists in a wide variety of forms, with additional verses. Most versions are similar to the actions used in the rhyme "Oranges and Lemons". The most common is that two players hold hands and make an arch with their arms while the others pass through in single file. The "arch" is then lowered at the song's end to "catch" a player. In the United States, it is common for two teams of those that have been caught to engage in a tug of war. In England until the nineteenth century the song may have been accompanied by a circle dance, but arch games are known to have been common across late medieval Europe.