The UK Deed Poll Office have just published a complete guide on how to change your name on your British passport.
It covers:
The most common reasons people change their passport name (married, divorce, gender) When a deed poll is required and when it isn’t How to apply online or with a paper form, including the costs involved The required documents and where to get support from HM Passport Office Special rules for children, newlywed passports, and gender recognition casesYou can read the full guide here: https://www.ukdeedpolloffice.org/passport-name-changes/
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