FBW
Just to clarify even further most of the 'ID Cards' carried by Brits living in other EU countries are actually residence permits and they aren't valid forms of ID and are not supposed to be used for crossing borders, in practice they look the same though and are commonly used for both ID and border crossings.
Most holders of these cards are not aware of the difference and think they are ID cards, the give away is normally the ministry of issue, being different to the one that issues normal ID cards. In most countries ID cards are issued only to those who would also be eligible for a passport, everyone else gets something a little different from the Ministry for Foreign Affairs.