There is no such thing as “international copyright” that automatically protects an author's writings throughout the world. However most countries offer protection to foreign works under certain conditions that have been greatly simplified by international copyright treaties and conventions.
The UK is a member of several international conventions in the field of copyright
Berne Convention for the Protection of Literary and Artistic Works
Rome Convention for the Protection of Performers, Producers of Phonograms and Broadcasting Organisations
World Intellectual Property Organisation (WIPO) Performances and Phonograms Treaty (WPPT)
WIPO Copyright Treaty (WCT)
Copyright material created by UK nationals or residents and falling within the scope of one of these conventions is automatically protected in each member country of the convention by the national law of that country.
Most countries (including all European states) belong to at least the Berne Convention and/or TRIPS which is a World Trade Organisation (WTO) agreement.
The Berne Convention provides that works will receive automatic protection without formality. However, you may choose to mark your work with the international © symbol, followed by the name of the copyright owner and year in which the work was created. In some countries (such as the USA), there is an official register of copyright which you might want to use, although registration is not an essential condition for copyright to subsist in any Berne/TRIPS member country.
The TRIPS Agreement obliges WTO members to comply with the Berne Convention (although some least developed countries have until 2021 to bring this into effect).
The Rome Convention and the WPPT provide some protection for performers, producers of sound recordings and broadcasters, while the WCT enhances certain protection provided by the Berne Convention. The number of countries that are members of these conventions is more limited than Berne/TRIPS.
A list of countries that belong to the different conventions is available from the World Intellectual Property Organisation (WIPO) and the WTO (for TRIPS).