There are only a few reasons as to why, legally, the public and press can be excluded from a meeting. The Public Bodies (Admission to Meetings) Act 1960 Sec 1 (2) states "A body may, by resolution, exclude the public from a meeting (whether during the whole or part of the proceedings) whenever publicity would be prejudicial to the public interest by reason of the confidential nature of the business to be transacted or for other special reasons stated in the resolution and arising from the nature of that business or of the proceedings; and where such a resolution is passed, this Act shall not require the meeting to be open to the public during proceedings to which the resolution applies."
It is generally considered acceptable to exclude the press and public if the agenda item relates to the consideration of tenders, leases, purchases of assets, for matters relating to staffing covered by the data Protection Act and to consider complaints against the council or a code of conduct complaint.
I would suggest that the matter you are referring to is a complaint against the council and they are therefore able to close the meeting to discuss their next steps, whether they need to seek legal advice or to agree a defence.