In general, I would think not. Excluding the public must be done by a resolution and the reason for exclusion must be stated in the resolution. Possible reasons are that the item would prejudice the public interest by reason of the confidential nature of the business or for some other reason. The confidentiality principle is usually taken to mean that the council can exclude the public where a duty of confidentiality would otherwise be broken. But it is not sufficient for the council to simply prefer confidentiality. Other reasons would include the discussion of most employment matters, or discussion of a commercial or legal matter where publicity would damage the council's ability to function properly. It's clear how keeping these matters confidential is in the public interest.
The practical effect of this seems to be that if setting a budget might give too much information to a potential contractor and thereby disadvantage the council and the citizens, then there would be a reason for exclusion. (Although the final decision must still be minuted, so some ingenuity might be needed to disguise the information). On the other hand, a consideration that the setting of the precept could be controversial would not be an adequate reason for excluding the public.
