Twilight Spain

[StainlessSteelCynic]

Considering that it has a permanent British population (military and civilian) and has elements stationed there from all three of the British Armed Forces, it's unlikely to be completely ignored by the British even if they can't project power overseas - until it gets nuked that is.
It plays a significant role not simply by controlling access to the Mediterranean but in British military communications in the Med and Northern Africa (both of which are highly likely the reason it gets a nuke in the first place)

It's not self-sufficient but it has a fairly healthy relationship with Spain in terms of purchasing goods & services from Spain and also employing Spanish locals.
With that in mind and as a bastion of British military force in the region it's likely to be attractive to Spanish people in the vicinity as a refuge from lawlessness etc. etc. - until it gets that nuclear warhead or two.

I'm inclined to think that after being treated to a nuke, there wouldn't be much left worth worrying about so that the British government could safely ignore it (even to the point of forgetting about it completely).
But the reason I mention all of the above is that, as long as any attacks don't render it completely destroyed or uninhabitable, Gibraltar makes an interesting adventure location that could be expanded into something akin to the Free City of Krakow (with the bonus of having waterborne adventures)