Currently UK child passports do not carry the names of parents in print despite this information being required to apply for a passport. As a consequence, parents who do not share the same surname as their child are often asked for additional proof of identity to confirm they are the parent.
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Travel with minors can be challenging for parents who do not share a surname with their children. As mum to two children who carry their father's surname - different to my own - I am frequently questioned at passport control when travelling alone with them and asked to show birth certificates to prove that I am their mother. Other child passports, for example Italian, carry both parents' names and data, which resolves this issue and is a more secure solution to establish the identity of parents travelling with minors.