Everyone has powers of arrest; the citizen's arrest. However, that is strewn with elephant traps.
"Any person can arrest a person who is in the act of committing an indictable offence or
Anyone whom he reasonably suspects to be committing such an offence, if
it is not reasonably practicable for a constable to make the arrest instead and
there are reasonable grounds for believing that the arrest is necessary, for one of the following reasons:
To prevent the person in question:
causing physical injury to himself or any other person;
suffering physical injury;
causing loss of or damage to property; or
making off before a constable can assume responsibility for him."
As everyone here well knows, an indictable offence is one that is tried at Crown Court. 'Not being in possession of a plastic bag', from memory, isn't in the list.