There seem to be issues on two levels here.
First, a council cannot make a decision except in a properly constituted meeting, by a vote of those present. The business to be discussed must be clearly described in the agenda. It must be clear what the council is deciding, so it cannot be right to decide something whose wording only exists in documents not put before the meeting. Supporting documents for a meeting should be made public along with the agenda, and if not made public would certainly be open to a Freedom of Information request. Decisions must be recorded in the minutes, and only decisions that are recorded in the minutes can be deemed valid decisions. Citizens have a statutory right to inspect minutes. The minutes must be clear about what has been decided.
Second, there could well be an argument for obtaining the emails under a FoI request, as you suggest. It is plain from past statements by the Commissioner that emails in a "private" account can be subject to FoI requests, where they are part of the documentation for a public authority. With limited exceptions, council meetings must be held in public. If email discussion is taking the place of discussion at a meeting, I would think there is a strong argument that FoI applies to the emails.
Really, I think the council should not proceed in the way described. Most councils do not do this. Good luck in mounting a challenge by all means possible!