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The United Kingdom, formed in 1801, comprises Great Britain plus Northern Ireland; the present Republic of Ireland was included until 1922. The constituent countries of the U.K. are England, Scotland, Wales, and Northern Ireland.
In both captions and text, typically spell out on first use; after that U.K. (including periods) is acceptable. U.K. is preferred adjective, even on first use:
chief U.K. export