Technically, he would be Charles I, of Britain. Charles I and II were kings of England!!
I'm not so sure about this statement. Remember that Charles I's father, James I, was originally James VI of Scotland before the throne passed to him after the death of Elizabeth I. Charles I attempted to force the English prayer book and the Episcopal form of church government on the Scots, which led to the Bishops Wars of 1637-38, and indirectly to the Civil War, as Charles I needed money to fight the Scots (who were not rebelling against the King, but for their rights to worship as they saw fit). Charles II, his son, was crowned as King at Scone in 1650 after returning from exile in Europe during Cromwell's dictatorship. Both monarchs named Charles were members of the Stuart family, and the Stuarts shared the thrones of England & Scotland until the Act of Union between the two nations in 1707.

So, yes, Charles would be Charles III, although his mother is technically Elizabeth I of Scotland.

Cheers,

Todd