What is the capital city of the United Kingdom?

London is the capital city of the United Kingdom and has been the political, economic, and cultural centre of the country for centuries. It hosts the UK Parliament, the official residences of the monarch, and numerous key institutions, including the Bank of England and the British Museum. London is also known for its significant historical landmarks, such as the Tower of London, Buckingham Palace, and the Houses of Parliament, which further cements its status as the capital.

The other choices represent important cities within the UK but do not hold the status of the capital. Manchester and Birmingham are vital urban centres known for their industrial heritage and influence in the UK's economy, while Edinburgh is the capital of Scotland, with its unique cultural and historical significance. Thus, London stands out as the definitive capital city of the United Kingdom.