Whether a council meeting is extraordinary or not has no effect on how it should be conducted, including the requirement to give proper notice and publish an agenda. The question of being "extraordinary" is simply to do with how the meeting comes to be called.
So, given the usual rules, if notice was not given at least three clear days ahead and no agenda was published, whatever meeting took place could not lawfully make any decision. There is thus some question over whether the extra meeting was actually a council meeting at all.
If it had been a council meeting, then the public cannot be excluded from the whole meeting, but only excluded from specific items on the agenda by a resolution passed at the meeting by the council and giving (in broad terms) the reason for the exclusion. Members of the public are entitled to be present until such a resolution has been passed, and are then excluded from the specific items covered by the resolution.
Opinions differ about informal meetings. Some argue that they should not happen. A middle of the road view might be that it is difficult to explore complex issues at a normal council meeting. If extended discussion is needed, this may be better achieved by a group of councillors meeting as a working party. In this situation, they cannot make decisions on council matters, but they can bring forward proposals for the council to consider. If the matter under consideration is of wide public interest, then it may be advisable to include some non-councillors in the discussion. It is certainly good practice for a council to allow some opportunity for members of the public to express their views, and to take them into consideration.
