The procedure is to put a motion to exclude the public and vote on it. Unless your standing orders say otherwise, you can do this without prior notice, although it is helpful for the public if they are warned in advance by an agenda item. Usually, an item of this kind is put to the end of the agenda to avoid pushing the public out of the meeting part way through, although this is not a legal requirement. If your standing orders require advance notice, you can still vote to suspend the relevant item, since it is not legally required.
A sound reason must be given in the motion to exclude, although there is no requirement to go into so much detail as to defeat the object of exclusion. For example, if the discussion would involve breaching an obligation of confidentiality, then the public must be excluded. Likewise, an employment matter is likely to require exclusion. It is undesirable to exclude the public without solid reasons.
Any decision made after exclusion must still be minuted, although this may be done with as little detail as possible consistent with recording that the council has made a decision and what that decision is. Decisions can only be made on agenda items, as is generally the case. There is never a requirement to record the debate in the minutes. Electors have a right to inspect minutes.
