999tommo - as I wrote, this is hypothetical and knowing the answer interests me, hence asking the question.
I can imagine a situation in which it may well occur: for example, the magistrate witnesses a breach of the peace and summons the police. But, by the time the constable arrives the breach of the peace has ended. For the constable to make an arrest, he would have to witness the breach of the peace himself, or have reason to believe that a further breach was likely.
The magistrate, having witnessed the breach of the peace could swear to that effect and could reasonably desire the offender to brought before a court to answer the charge. One could therefore imagine a situation in which it would be desirable for the magistrate to see the offender arrested, but which the constable could only do with a warrant to that effect.