According to the Gov.uk website, new rules will apply for travel to Europe if the U.K. leaves the EU without a deal. U.K. citizens are being advised to have at least six months left on their adult or child passport when traveling to most countries in Europe (not including Ireland) after the U.K. leaves the EU. It is advisable to renew your passport before traveling if you do not have enough time left on your passport.
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Do Britons need a new passport after Brexit?
If a no-deal Brexit happens at the end of January, what travel documents do I need to apply for as a U.K. citizen in order to travel in the EU?