@Xavier , British Overseas Territories are also not part of the U.K. either.
They are self-governing except for the following things;
Governors are always appointed by London - as they viceregally represent the King.
Defence is a matter for London.
Foreign affairs is also a matter for London as well.
Internal affairs are matters for the British Overseas Territories themselves.
The British Crown Dependencies have Lieutenant-Governors to viceregally represent the King.
Aidan.