As an example Special Constables have full powers of arrest in their county and any adjoining county (whether on or off duty). They do not have powers of arrest or detention outside of those areas. They hold a warrant card as a member of their counties force. Paid officers have powers of detention and arrest anywhere in the UK.
Incorrect - please refer to SOCAPA 2005. Special constables now enjoy the same powers and privileges as their regular colleagues.
Either way - challenging the authority of a constable of any authorised person isn't going to go down too well. Also note that EVERYONE has the power of arrest in this country for a relevant offence.