There are no set rules about a letter of no confidence. It has no formal role in council affairs and will not have any specific result. That being the case, you can be guided by questions about what effects it will have.
The kind of purposes that might be met by a letter of no confidence are both direct and indirect. The direct impact could be to cause at least some councillors to consider what is happening in the council and how things might be done better. It could prompt some councillors to consider resigning, which would allow citizens to put up alternative candidates and perhaps demand a poll. Indirectly, the letter can be publicised, such as through local press, or other local channels. That may generate helpful public interest and further action.
What will work best is thus a matter of judgement as to which of these possible goals are the most important, and what will, in the circumstances, have the greatest effect. It is quite likely that the letter will need to be only one part of an ongoing campaign.
