You only need "the" if there is a common noun in the name of the country. I'll write the common noun in CAPS: the United KINGDOM the United STATES of America Britain France the NetherLANDS Spain Europe Asia (North) America The Americas (in this case you're talking about 2 continents, so you need "the")

Britain/Great Britain/England/Wales/Scotland = no article. But we do say THE British Isles. THE United Kingdom. I live in THE British Isles. I live in THE east of England, in Cambridgeshire. My grandparents were from Scotland. My family have always lived in THE British Isles.

Britain is a given name (a proper noun), so no "the". Yes, we use "the UK / the United Kingdom".

Thank you:D!