It's the excuse the police use to arrest people who want to make a point at a protest. If your "presence" could lead to the larger group getting annoyed with you, then the police can say that your presence could cause a breach of the peace.
EXPLAINER: Anti-Monarchy Protests - Liberty (libertyhumanrights.org.uk)
A man was also questioned by police, asked for his details, and threatened with arrest under the Public Order Act 1986 on Monday 12 September, after he held up a blank sheet of paper in Parliament Square – on the basis that he was intending to write ‘not my king’ on it and this “may offend people”. This came after a woman holding a piece of paper reading ‘not my king’ outside Parliament had been led away by police and asked to stand on the other side of the road, but was not arrested.
‘Breach of the peace’ is not a criminal offence in England & Wales, and you cannot be charged with or convicted of it. Instead, the police have the power to arrest you where you have breached, or are about to breach, the peace, and you may then be subject to a court order requiring you to refrain from breaching the peace.
The arrest must only be for the purposes of preventing a breach of the peace or bringing it to an end. Therefore, the police must release you once it is clear that you no are longer breaching, or about to breach, the peace. If your behaviour is lawful, but harm is still likely (e.g. because others might be provoked to commit violence), exercising the power of arrest must be exceptional – ‘only in the clearest of circumstances, and when they are satisfied on reasonable grounds that a breach of the peace is imminent.’
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