Vaguely.

The term comes from the time when the Royal Navy switched from other fruits (oranges if I recall) to limes as their source to avoid scurvey way back in the 17/18th C. It somewhat backfired as the vit C content of limes is pretty poor compared to oranges and other fruits. I believe that they switched to limes as that is what the British plantations in the Carribean were producing.

So you could call all Brits limeys yes, although originally it was a term reserved for the Navy, that I guess, transferred to all the armed forces during WWII.