I'm not really concerned that UK and the EU will start some WWIII against each other. What I'm more concerned with is that they will have differing policies for dealing with rogue states, and/or create competing interests in different regions of the world, especially the Middle East and Africa.

WWIII will probably start with what will look an awful lot like the Forth Crusade.

Edit: obviously I meant fourth, and I don't mean this from the religious perspective, just the European involvement in conflicts in the Middle East.