You’d have to be more specific about exactly what it is that causes concern. I’m going to guess strimming grass verges?
Many activities have specific requirements according to the nature of the activity eg, work in the highway / highway margin is likely to require signing, lighting and guarding, May require a ‘licence’ from LA and has specific PPE requirements for the protection of the worker and the highway user.
Work at height, work with machinery (hand arm vibration) , work where harm may be caused to others (spraying chemicals) all have very specific regulations and management of H&S requirements.
There is a hierarchy of compliance starting with high level statutory requirements which is distilled down through many levels to working level ‘guides’ and good practice documents based on industry codes of practice.
So generally, work based activities which carry an inherent risk of harm to the worker or to anybody the worker comes into contact with, are governed by H&SaWA.
There is also the Occupiers Liability Act which requires that land and property are kept in such condition as to not give rise to the risk of harm to others - whether invited or not.
Whilst lacking specific detail, if your Cllr thinks the council carries no liability for the actions of employed, contracted or even volunteer workers, then they are the liability!
Report, specifically, the detail of your observations in writing to the council.
There is limited potential for mitigation for damage or harm caused when it is possible to show that the responsible entity was reasonable unaware of the situation prior to it occurring.
If there is a written record of a report of reasonable concern, that potential mitigation is removed - this may be significant in a subsequent civil or criminal action and it would be considered by HSE investigation.