In england-and-wales (and some other jurisdictions) there is the concept of 'implied licence' or implied permission to be on someone else's private land. It is a type of 'bare licence'.
4.2 A bare licence is a personal permission, given otherwise than for consideration, to enter or be present upon somebody else's land. The grant of a bare licence performs the minimal function of providing a defence against the allegation of trespass - and even then only so long as the licensee does not overstep the ambit of the licence conferred (see e.g. Tomlinson v Congleton BC (2004) at [52] per Lord Hutton, [67] per Lord Hobhouse of Woodborough). In the famous phrase of Scrutton LJ, '[w]hen you invite a person into your house to use the staircase, you do not invite him to slide down the bannisters' (The Carlgarth (1927)). ...
4.3. A Bare licence can be created purely orally and may arise either expressly or impliedly. ...
Similarly [to the occupier of a dwelling-house], business premises are usually the subject of an implied licence permitting entry by members of the public for commercial or consumer purposes (but not, for instance, for the purposes of skateboarding ...
- Land Law by Kevin J. Gray, Susan Francis Gray, pages 97-98
Although you might not have been personally or explicitly invited to be on the land, you don't commit trespass so long as your behaviour is within the implied licence or any conditions printed on a sign or such.
Fundamentally this is about socially acceptable behaviour or legitimate business, such as you entering a neighbour's land to knock on their door for an innocent purpose (borrowing/lending something, asking about their well-being, giving them/asking for a package left with you/them etc) or entering a shop to browse or buy. You commit trespass if you enter your neighbour's land to use their barbecue and hammock without their permission.
A letterbox in your front door gives postmen implied licence to deliver letters through it - they don't commit trespass when entering your land to make a delivery. There's no implied licence to push rubbish through the letterbox. (For people unfamiliar with a letterbox, essentially it is a slot in the door - it can be made more complicated.)
A shop or shopping centre open to the public gives visitors an implied licence to shop (to browse or buy). There's no implied licence to enter the premises to disturb shoppers/the business or vandalise things etc.
If you really must have intent to shop (not intent to purchase) in order to justify entering a public business wouldn't that technically make all sorts of common activities illegal? Entering simply to use the bathroom, going to gamestop just to play video games on the display console, etc
It may well amount to trespass (a civil wrong or tort, not a criminal offence) to enter a shop just to use their toilet, loiter, play videogames, sleep on a mattress in mattress shop etc, set alarms of display mobile phones, or such.
The proprietor may put up signs that define conditions to be on the premises or certain areas of the premises - i.e. limits of the licence. E.g. "toilets are for customers only," "wi-fi is for customers only" or "be quiet while in the library".
Entering/using the premises for a purpose outside the implied licence and/or explicit terms is a trespass but the proprietor might not be aware of it. Even if the proprietor were aware, they may not care - they might welcome the footfall, given it may represent an opportunity to do business that would not exist if the visitor weren't present. Even if the proprietor were aware and did care, they might only ask you to leave and not immediately 'go legal'.
Generally speaking, it's up to the proprietor if she wants a visitor to leave and if a visitor refuses then there is no doubt they are committing trespass - they have explicitly or expressly lost permission to be there.
Committing trespass and intentionally obstructing, disrupting, or intimidating others from carrying out lawful activities is aggravated trespass, at s68 Criminal Justice and Public Order Act 1994.
Some protesters have been found to have committed trespass or aggravated trespass on shops premises (e.g. inside shops or petrol station forecourts).
