Formal Japanese name for the United Kingdom of Great Britain and Northern Ireland. In everyday conversation, イギリス is far more common.
See also: イギリス
The United Kingdom consists of England, Scotland, Wales, and Northern Ireland.
イギリス is the everyday word for the UK (and sometimes loosely for Britain or England). 連合王国 is a formal, official name rarely used in casual speech.
英国 is a common abbreviation for the United Kingdom, used in compounds like 英国政府 (British government). 連合王国 is more formal and less common.
Compound of 連合 (union) and 王国 (kingdom), directly translating 'United Kingdom'. The kanji 連合 is a modern simplification of 聯合.