In the UK, Alice burns a Quran on a public pavement.
Bob tears up an Irish flag.
Do either of these commit public order offences?
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Or, at least, not of itself, but it could be part of a pattern of conduct that is.
The Crown Prosecution Service defines a public order offence as an act that involves the use of violence and/or intimidation by individuals or groups.
bdb484's answer that "neither is a crime in and of itself." is not quite right, and in a way, the answer for the US is the opposite: burning a book, in and of itself, can be criminalized, but criminalizing the reason for doing it raises constitutional questions. There is absolutely no constitutional bar to a generally applicable, content neutral law against setting things on fire in public. It's only when the book-burners are treated differently based on what their bonfires express that free speech comes up. So if a Quran burner is prosecuted, but a phone book burner is not, then the Quran burner has a constitutional argument available to them.