It seems like Brexit may have brought about a change and now all Commonwealth citizens can register yachts on the UK Ship Register under Part 1. It costs £153 to register for 5 years plus you'll require a certificate of survey for tonnage and measurement. If you're in the UK, the RYA will do a tonnage survey for £145.00 up to 15m and £185.00 over 15m. Don't know about tonnage survey costs elsewhere.
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The Merchant Shipping (Registration of Ships) (Amendment) (EU Exit) Regulations 2019.pdf