He obtained British citizenship, before his marriage through a special scheme for those who had served in the UK armed forces.
However, the 1705 Sophia Naturalisation Act made all descendants of Sophia of Hanover British subjects and Philip was such a descendant. It was repealed in 1949, but Philips cousin, Ernst Augustus successfully obtained citizenship on this ground (albeit after a legal battle).
Yeah lots of Philip questions today, I have been reading up on him, being bored.
Plus (though I have no idea if this was in anybody’s calculations) it did him no harm in the PR stakes if his recent war service was emphasised, rather than an older work-around of the dynasty’s German connections.