The term "normal gauge" is a very relative term. If we focus on England, there are two gauges in history which competed with each other in the nineteenth century.
2134 mm, now known as the Brunel gauge. The big companies that used it included Great Western. It was used there until 1892.
The 1435mm gauge used by Stephenson, who was a great promoter of it. 
In England, unification was achieved in 1892 with the passing of the Railway Act.

In Ireland the standard gauge is 1600 mm