99% of the UK population has no idea we have a base in Cyprus and they sure as hell wouldn't go to war over it - and, as I pointed out earlier, you forget the Cypriot Govt are also are a player.
A threat from Russia could/would lead to a request that the UK should leave - or at the every least not use the base. Either would be almost impossible to deflect
and as westernhero said NATO isn't going to go nuclear over say a Russian cruise missile strike on 4 Tornado GR's at the end of the Med...........