As an ex cop no they don't have the same rights as the police.
They are there as a deterent to look like Police.
they only have the same arrest rights as any member of the public, which is limited to arrestable offences. Do you know what they are?
Any person who is in the process of committing an offence.
Any person the arrestor has reasonable grounds for suspecting is in the process of committing an offence.
Any person who is guilty of an offence previously committed.
Any person the arrestor has reasonable grounds for suspecting has committed an offence previously.
and
It is not reasonably practicable for a constable to make the arrest instead
and to prevent one of the following
The person causing physical injury to himself or others
The person causing loss of or damage to property
The person making off before a constable can assume responsibility for him.
These powers are rather risky to use, since it relies upon the person carrying out the arrest knowing that an indictable or either way offence has been committed — if, for example, the person they arrest is later acquitted in court, then no offence has been committed, and so the arrest was unlawful. In addition to the above, a private person may be authorised to execute an arrest warrant, if the court issuing the warrant has given them the authority to do so, and any person may arrest someone who is "unlawfully at large" (for example, an escaped prisoner).
