You’re mostly right, the country became the Kingdom of Great Britain after the Acts of Union 1707, including England (with Wales) and Scotland, although ‘UK’ (as in United Kingdom of Great Britain and Ireland) didn’t come into being until the Acts of Union 1800 (which were passed by the parliaments of both Great Britain and Ireland in 1800, but came into effect at midnight on January 1st 1801). So, the answer ‘Great Britain’ is correct, but ‘UK’ is not.