Indeed. It would be, for the UK. And as a result it would seek as much inside information and influence as possible. No EU member (with the exception of Malta perhaps) is both Britain-friendly but also small enough to allow not merely a peek inside but also influence on EU policies. In other words, Cyprus would cease being just a geostrategic rock in the the eastern Mediterranean loaded with all kinds of "sovereign" critical surveillance and mission enabling infrastructure, but it would also become an extremely attractive political ally, in the true sense of the word.
All the UK has to do to maintain its geostrategic privilege of the military bases is smile. The "sovereignty" bit makes it so. But for the political privilege the British would have to do a great deal more than smile. They would have to give. And it so happens we have something to ask for in return. Urgently. Freedom from 60's & BBF's political apartheid and 74's geographic division. The smiles would no longer cut it for the natives.
Source: My Facebook wall