Good point by @stevesb about the commercial purpose of the flight is not just the whether the pilot is paid. However, one of the ‘non-commercials’ examples used by CAA is local authority own staff member flying their own drone for there own needs. a a local authority is classes as non profit and you are ‘volunteering for them’ I would suggest not commercial.
Agree about checking whose public liability insurance is covering, as Local Authorities normally require £10 million in any procurement tenders, regardless of the service being provided. Again, if pilot is classed as volunteer for the council, then this is covered by council insurance, but just need to make sure that includes UAV flights.
I would also expect them to want a full risk assessment, the council I worked for, until recently, even required groups doing beach cleans to have a risk assessment and insurance.
Major part of the PfCO course is flight planning and risk assessments is a key element. @suffolkfox I can send you my generic flight risk assessment if you would like, and site survey and site specific risk assessment templates.