If the relevant park / play area is owned or leased by the council then they can enforce their own parish bye-laws.
These bye-laws can only be enforced (i.e. fines issued) by an authorised officer of the council or a constable.
This means that whilst councillors could collect evidence (as could any member of the public), they could not fine anyone, only the authorised officer (the parish clerk or any staff employed - and authorised could do so), or a police constable.
For this reason, bye-laws that create offences must be approved by the MHCLG and your local police authority.
In a small parish, I would be careful of parish councillors going around photographing people - as opposed to talking to them - you don't want to create an, easily created, animosity between the village and council.