JimJools' reply is incomplete. Britain is within the EU but has a closed border toward all other EU countries except Ireland. If you are a non-EU citizen then you do not have a British passport and having one would not confer on you any more rights than one from the other EU states, in fact arguably less because Britain is not within the Schengen area (in the event that Schengen insisted on visas from non-Schengen including Britain, then only Britain would be open to you without a visa). If you are currently in the UK you can leave at any time on a valid passport and the same holds wherever you are currently. If your passport is from any of the countries that have bilateral agreements with the EU then you are free to travel within the EU, but some restrictions on the length of stay may apply. If your passport is from a country within the EEA or from Switzerland then you will be entitled to unrestricted travel within Schengen including the whole of the EU. If your passport is from a country other than those indicated above then you can only travel when in possession of a valid visa.