Breach of the Peace is not a criminal offence: you can be arrested, but you cannot be charged.
The police have the power to detain or arrest you if a “breach of the peace” has occurred, or to prevent it from occurring. A breach of the peace is defined as “an act done or threatened to be done which either actually harms a person, or in his presence, his property, or is likely to cause such harm being done.” They must release you once the threat of the breach of peace has passed.
If arrested for breach of the peace, you should not give any personal details. The police will try and persuade you to do so, but you are not legally obliged to give details (or DNA or fingerprints). Because you must be released once the threat of a breach of the peace is over, even if you have not given your name and address, that cannot be a reason for the police to hold on to you.
The police sometimes use this power to arrest groups of people at actions, drive them far away from the site of the action, and then release them in the middle of nowhere (without ever going near a police station).
If the police deem either that you have actually committed a breach of the peace or that your release is likely to cause a further breach of the peace, then you can be held overnight and put in front of a judge to be “bound over” for a period of time and some cash, approx £100. Basically this means you agree to ‘keep the peace’ for a certain period of time and agree to pay the specified sum if you do not keep to the agreement. This is not a conviction and will not be put on your permanent record. If you refuse the bind-over you can be jailed for contempt of court for a few weeks or until you agree to it.
Please note: The above advice applies to England & Wales. Breach of the Peace is very different and much more serious in Scotland.