If we have another King James (such as https://en.wikipedia.org/wiki/James,_Viscount_Severn could be a possibility, but monarchs don’t have to take their first names), as there’s already been King James I & VI and King James II & VII (the grandson of King James, he took the throne after his brother Charles II (restored monarch to the throne after Oliver Cromwell died, and son of Charles I (who was beheaded) who was son of James I & VI) died without a legitimate heir (though apparently he had 12 illegitimate children)) he would be King James VIII but not King James III because it was changed at one point when Ireland, Scotland and England (in 1746 Parliament passed the Wales and Berwick Act which means in all prior laws England meant Wales and England so I’m not ignoring Wales) became the United Kingdom in 1707 (though later on the Republic of Ireland gained independence) and so the thrones were combined.

Generally people would use the English number to refer to the royal, because it’s tended to be the higher number, but Winston Churchill decided (it’s not a ruling, just a suggestion) the higher number should be used. So Queen Elizabeth is known as II (though she did have some post boxes destroyed in protest in Scotland, as they never had a Queen Elizabeth I) but a future King James would skip all the way to VIII in England. https://en.wikipedia.org/wiki/Regnal_number#Ordinals_and_the_British_Acts_of_Union_1707