IANAL, but I have fun with a DSLR, and educate myself on what I legally can or can't do with it.
IAAL and you have fundamentally misunderstood what has happened here. Since you like to educate yourself, I'll share some of my precious time ;)
This is not happening pursuant to any general laws relating to photography, which are probably quite similar in the UK and the US, but under under contract law.
As I understand this situation... When the occupant (that is the resident owner, or leaseholder) of private property (eg. a shopping centre) sets conditions of entry, and displays these conditions of entry in a place visible to the entrant, the entrant is taken to have agreed to those conditions by virtue of entering the premises. The quid pro quo here is that you agree to be bound by the conditions of entry, in return for an undertaking by the occupant not to sue you in trespass.
This is, for example, what gives supermarkets the "right" (it isn't a right, you've just given permission) to search your bags where this is stipulated in the conditions of entry.
The shopping centre in question apparently made it a condition of entry that no photographs be taken by entrants. And this gentleman was apparently in breach. I have not read the conditions of entry, but they may have included an agreement to surrender all " ... equipment; film; and other media to Capital Shopping Centres Group PLC or its authorised agents" on breaching said condition.
I doubt that this works very differently in the US, the UK or indeed any other common law country, (although there may be some variance as to what limits the various legislatures have set as to what contractual conditions might be enforceable).
Confiscation of cameras in the US is theft.
"Confiscation" without a statutory right of confiscation (as some LEOs may have) or the consent of the owner, has been a common-law crime in Britain since at least the 12th century and a statutory one since the 19th, known variously as 'larceny' and 'theft.' Without reading the actual conditions, however, we don't know whether or not the gentleman in question had agreed (albeit unwittingly) to hand over his camera.
The story, I'm led to believe, has a happy ending, the corporation in question having agreed to remove this onerous condition.
The larger problem --the privatisation of the High Street and the concomitant abrogation of individual rights this involves --is, in the face of the relentless invasion of the mall, unlikely to be so happily resolved.
I'm a law student and while I agree with the fundamental points which you make here but I do have some concerns regarding the onerous (a legal term which means, in this context, unfair) terms set out in these supposed notices.
I believe that it was in Thornton v Shoe Lane Parking where Lord Denning said that some terms are so onerous that you would have to have those terms printed in big red letters with arrows pointing towards them (bless him).
In Olley v Marlborough Court Ltd an exemption on the part of the hotel (in the case) was not held to give rise to an exemption because the notice was presented too late. To apply this to this case I should think that the notice would have to be a quite large sign (large enough to be noticed by a reasonable man taking reasonable efforts) on the outside of the mall - that is to say before entry as entry would constitute offer and acceptance and the contract would be formed (you would at that point have agreed to the terms). If they didn't go to reasonable lengths to inform this man and his child (the sign wasn't sufficiently large or something like that) then Parker v SE Railways Co may give relief.
Does this make any sense?