It's a tough job being clerk! And councils must conform to good employment practices. But sometimes action has to be taken. Different councils have different procedures for handling problems. The chairman usually has a key role, but it is also common to have a staffing committee so that matters are not in a single pair of hands. Ideally, there should be written procedures for dealing with disciplinary matters and grievances, and these should provide alternative routes.
From your description, the council is in a mess. If a chairman has not been properly appointed, then it appears that the council cannot lawfully function, and so any decisions that purport to have been made are invalid and could be challenged. However, it is difficult to challenge unlawful acts by local councils because it usually requires High Court action, with the attendant substantial expenses. So unless the matter is especially important to someone, actions are rare. A factor that could affect councillors' decisions is that there could be a risk of opening up personal liability for costs incurred without lawful decisions to back them up, although this would most likely have to involve demonstrable negligence.
All this is getting into areas where professional advice should ideally be sought. However, a good first step could be to try to involve the senior legal officer of your district council. They do have a role in relation to the proper running of local councils (although their powers are limited) and other councillors may take notice of a firmly expressed opinion from the district's senior legal officer. They may be more inclined to take a stand if approached by a group of councillors rather than an individual. Cost won't be a factor, at least initially.
