Olsen
Well-known
The public enters with the understanding and awareness that they are on private property where the rights of the property owner take precedence. Mall owners can legally ban photography just as they can legally prohibit someone from pitching a tent in the food court and taking up residence.
The issue with malls and other businesses is the seemingly selective or biased focus on photographers using more noticeable equipment, such as SLR's with long lenses. People with cellphones and p&s cameras do not appear to drawing attention.
In addition, that issue -- businesses and private security guards without police powers -- needs to be considered separately from hassling of photographers in the UK and elsewhere under the auspices of legislation that legitimizes the police behavior.
I come from a country where free roaming is allowed and private property do not have this stringent protection as in the UK or US. Still, as you point to; private security guards could 'make trouble' for just anyone. The measure over here is to 'call the police'. They will most often sort out any problem and tell guards to cool it if it is about as silly an issue as photography.
That said; we are not allowed to photograph strangers on the street here without their consent. Still we do it. Most often without any problems whatsoever.