If you were travelling from the UK to these places, then yes you should have your passport checked. But for example if you fly from Spain to Italy or drive from Germany to France, you will not have your passport checked.
The UK is not in the Schengen arrangement. There are no border controls at all between Schengen countries.
I think the UK and Ireland are the only EU countries outside Schengen. Could be wrong about that though.
Right, got it now, cheers.