to the entire country and is not personal to individuals.
A Magistrates' Court may "bind over" a person to "keep the peace" and this power stems from the Justices of the Peace Act 1361. The court may bind over a person either following a complaint (Magistrates Courts Act 1980 s115) or of its own motion. Binding over has been a pragmatic method of dealing with those responsible for minor disturbances. A binding over is not a criminal conviction. A sum of money (the recognisance) is set but does not have to be paid there and then. However, if there is a further breach of the peace within the stated period of time then either the whole of part of the recognisance will usually have to be paid. Binding over seems to have declined in use due to penalty notices for disorder and the possibility of prosecution under the Public Order Act 1986.
This common law power undoubtedly gives the Police greater flexibility not only to deal with disorder but to prevent it occurring. However, the concept of "the peace" lacks the precision and certainty which statutory powers normally have. In Albert v Lavin  AC 546, Lord Diplock stated - "... every citizen in whose presence a breach of the peace is being, or reasonably appears to be about to be , committed has the right to take reasonable steps to make the person who is breaking or threatening to break the peace refrain from doing so; and those reasonable steps in appropriate cases will include detaining him against his will." Here then is high legal authority for the power to arrest not being just a Police power.
Extensive case law exists in this area but it seems to establish that there must be some element of actual or possible disorder however slight. In R v Howell  QB 416 it was held that the behaviour that caused a constable to believe that a breach of the peace had or would occur had to be related to violence and such a breach occurred whenever harm was actually done or was likely to be done to a person, or in his presence to his property, or a person was put in fear of being so harmed through an assault, affray, riot, unlawful assembly or other disturbance. The case of R(Laporte) v Chief Constable of Gloucestershire  UKHL 55 contains a full discussion of the law. An important aspect of this case was that it was not enough for the police to apprehend some future breach. The apprehended threat must be imminent though what counts as "imminent" depends on the context. See also the later case of Austin v Metropolitan Police Commissioner  UKHL 5 which was concerned with the police tactic of "kettling" as a result of which even persons acting lawfully were detained.
In Steel v U.K. (1999) 28 EHRR 603 it was argued that the common law power was inconsistent with the European Convention's principle of legality. However, this was rejected on the basis that there was a body of case law which had clarified the power to arrest for breach of the peace.
Plainly, the breach of the power is capable of adversely affecting freedom of expression (Article 10) and the freedom of association (Article 11). It is incumbent on the Police (as a public authority) to pay due regard to those rights and it is unlawful for them to act incompatibly with those rights (Human Rights Act 1998 s.6).
Interestingly, the idea of breach of the peace finds its way into some criminal offences. One example is the Theatres Act 1968 s.6- Provocation of breach of the peace by means of public performance of a play. This offence may only be prosecuted with the consent of the Attorney-General.
Public Nuisance: This is both a tort and a common law crime. An appeal against sentences imposed for public nuisance (sending letter bombs) was heard in R v Holliday and Leboutillier  EWCA Crim 184. The House of Lords considered "important and difficult" questions in R v Rimmington and Goldstein  UKHL 63. The magisterial speech of Lord Bingham of Cornhill is essential reading. It is worth noting his Lordship's words at para. 37:
"To permit a conviction of causing a public nuisance to rest on an injury caused to separate individuals rather than on an injury suffered by the community or a significant section of it as a whole was to contradict the rationale of the offence and pervert its nature ..... "
and later, Lord Bingham approved the conclusion reached in an article by Professor Spencer - "Public Nuisance - A critical examination" - Cambridge Law Journal -  CLJ 55:
"… almost all the prosecutions for public nuisance in recent years seem to have taken place in one of two situations: first, where the defendant's behaviour amounted to a statutory offence, typically punishable with a small penalty, and the prosecutor wanted a bigger or extra stick to beat him with, and secondly, where the defendant's behaviour was not obviously criminal at all and the prosecutor could think of nothing else to charge him with."
Arrest: from 1st January 2006 the law relating to arrest was altered by the Serious Organised Crime and Police Act 2005 ss. 110, 111 and Schedule 7. The power to arrest for breach of the police was retained. The revised powers of arrest are considered here and here. Basically, a constable may arrest a person for any offence but the constable must have reasonable grounds (an objective test) to believe that for any of the reasons set out in section 110(5) an arrest is "necessary." One reason is where the constable reasonably believes the arrest to be necessary to allow prompt and effective investigation of the offence or the conduct of the person in question. (Note: The 2005 Act inserted a new section 24 and 24A into the Police and Criminal Evidence Act 1984).
Returning to the 28th April arrests. Whilst the precise basis of the individual arrests is not entirely clear it seems that they were based on one of other of these common law concepts: breach of the peace or public nuisance and maybe with an element of conspiracy thrown in. The concepts lack precision but, in practice, seem to enable the Police to arrest almost anyone who is doing something which either they dislike or which they consider others will dislike. For all its antiquity, this is not satisfactory law in modern times. Given that the actual cases may come before the courts, this post expresses no opinion on the actual conduct of those concerned.
Leading text on Law of Public Order and Protest is perhaps that of His Honour Judge Peter Thornton QC et al. Oxford University Press - March 2010.