it is not a crime to occupy non-residential premises without the permission of the owner
Correct albeit with the following qualification:
The fact that the pub was not trading at the point of occupation does not appear to be relevant - is that correct? i.e. if a person were to stay past closing (or even when they were requested to leave) at a pub in England, is there nothing that the landlord could do to require the person to leave short of applying and waiting for a High Court order?
Whether the pub is trading does seem relevant, because you commit the criminal offence of aggravated trespass (s68 Criminal Justice and Public Order Act 1994) if you intentionally deter, obstruct or disrupt a "lawful activity" while you are trespassing.
A lawful activity is anything that isn't a criminal offence or trespass (s68(2) CJPOA 1994). Lawful activities can occur while the premises is closed to the public. E.g. shelf-stacking, tidying, cleaning, stock-takes, till checks, putting the cash in the safe, taking deliveries etc. (I don't know if locking up and going home would count?)
If a constable reasonably suspects you of aggravated trespass they can arrest you without warrant.
In addition, if a senior police officer at the scene reasonably believes you are committing aggravated trespass they can order you to leave the premises and if you refuse to leave that is a criminal offence in itself (s69(3)(a) CJPOA 1994).
There's also Failure to leave licensed premises (i.e. business that sells alcohol), s143 Licensing Act 2003:
(1)A person who is drunk or disorderly commits an offence if, without reasonable excuse—
(a)he fails to leave relevant premises when requested to do so by a constable or by a person to whom subsection (2) applies, or
(b) he enters or attempts to enter relevant premises after a constable or a person to whom subsection (2) applies has requested him not to enter. ...
Pub landlord could claim you are drunk and ask you to leave, then have security and/or the police back him up.
I'd have expected this to be happening a lot more than it does (e.g. those living on the streets could easily go into a shop during the day and be under cover at night).
I don't know if any of the above is in fact why people don't seem to "regularly move into trading premises and refusing to leave" but it shows there is more risk of (being suspected of) committing a criminal offence and being arrested than if they moved into unoccupied commercial properties.
Also, at common law, property owners (and their security guards) may use "no more force than is reasonably necessary" to remove trespassers. And s3 Criminal Law Act 1967 allows use of force to prevent crime. (Is the trepasser committing aggravated trespass or consuming or damaging anything that doesn't belong to them?) This seems more likely to be a risk in terms of occupied than unoccupied commercial properties.
I assume private security would not use force (as if they could, then it's not clear why they would not be able to do so in the reported scenario).
In terms of the reported scenario (unoccupied non-residential property) the law (s6 Criminal Law Act 1977) says that, while the squatters remain, the owner and police may not force entry unless the squatters have committed crimes or aren't complying with a Possession Order.
6 Violence for securing entry.
(1) Subject to the following provisions of this section, any person who, without lawful authority, uses or threatens violence for the purpose of securing entry into any premises for himself or for any other person is guilty of an offence, provided that—
(a)there is someone present on those premises at the time who is opposed to the entry which the violence is intended to secure; and
(b)the person using or threatening the violence knows that that is the case.
