Check your councils Code of Practice to see if anything has been breached.
Generally a councillor not acting as a councillor would not be subject to the Code of Practice. However some councils make it against the code to post comments on social media anonymously.
Or are you saying that the councillor was clearly operating as a councillor and its was the person he was commenting about that was anonymous? In that case you could make a complaint (providing the comment breached the code).