You don't need ANY ID to cross a EU country to another. None. Absolutely none.[/B]
As Spanish I can go anywhere without showing any ID. IF brits needs to show the passport, is because you are picking a plane. Is safety reason, nothing else. Also, from spain to UK, to UK to Spain, with the spanish ID is enough, not passport. But as I repeat, is because you are picking a plane. If a brit is in Belfast (UK) and want to cross to Irleand, they don't need ID because the "border crossing" is by land. If a brit wants to cross by land France to Germany, they don't need an ID at all but they need it if they fly
Also, freedom of movement is not only the right to go to a country without an ID, is the right to stay if you have some requisites to stay (and work, and vacations, etc...), without freedom of movement, this requisites will be much more restrictives