I have no idea about the UK, but there is criminal trespass in the US. If you’ve been warned not to enter a property, including by signage, but you do anyway, that typically is a crime for which you can be arrested here. It depends on the jurisdiction, but that’s true in most of the US. Same if you have been asked to leave a property and you refuse.
I wouldn’t advise that in the US, and not because the security guards are armed. Again, if they reasonably suspect you of shoplifting, they have a legal right to detain you. They can’t use an unreasonable amount of force to do that, but they can block the exit, for example, and if you try to use force to escape, they can then use force to prevent your escape. It would be a needless escalation that could land you charges of assault even if it turns out you didn’t shoplift (as long as their belief that you did was reasonable, which is a really low bar). By all means, though, pull out your phone and record.
