As far as I know there is no restriction on nationality, but you may have to become a British SUBJECT and you will have to swear loyalty to the Queen
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Bit of thread drift here, but I notice you capitalize the word 'SUBJECT'. Most of us ceased to be British subjects in the 1990s, I believe, and are now British citizens. However I think the term still exists for those who like yourself were not British subjects at birth, but who subsequently acquired UK citizenship. Is that the case as far as you are concerned - ie are you actually a British subject?