It's (theoretically at least) a criminal offence, under the Theft Act 1968, to remove something from a skip without the permission of the owner. However, that brings into question as to who the owner actually is. Does the householder still retain ownership or has he transferred such ownership to the company providing the skip?
To complicate matters further, it's not theft if the (former) owner of property has genuinely discarded it. So, for example, the tramp who rummages through rubbish bins on the street isn't committing theft.
So it's complicated. If you were placing metal items into the skip, and the skip owner was expecting to profit from the scrap metal value, taking those items would probably be theft because a court could rule that you'd simply transferred ownership of the metal, rather than discarding it. In that case, the court would probably order that any restitution be paid to the skip owner, rather than to you. However, the magazines and websites which promote 'skip diving' usually advise that, in order to stay on the right side of the law, the householder's permission should be sought before removing anything.
Chris