Well, if it is a military area, the situation is a little more complicated than a shopping area in view of all those "security" hullabaloo. I do recall having discussed the position at length for military places. That said, I would focus the discussion here on shopping centres since that is what the thread starter asked.
Also, there is a difference between acting gungho and actually knowing what your rights are. Building "regulations" are internally drafted rules and can never give the building owners a right of action which they never had.
Of course, if they put outside in a sign which says "No photography, if you choose to enter and subsequently take photographs, then you must hand over those photographs for deletion"; then their position MAY be stronger. But even so, I don't think a contractual right can trump over a property right. Hence, all they can do is to institute a civil action for breach of contract requesting for an injunction to compel the deletion of the photographs. The alternative is to prosecute for trespass. They will not be able to FORCE you to delete the photos without a court injunction.
One distinction to bear in mind and to make a clear difference, is between what is morally right and wrong, and what is legally right and wrong. Our moral compasses may tell us that this seems wrong, or that seems right, or "I think it sounds right that this guy can do this". However, this often does not gel with what the actual legal position is.