Representatives from the Anglican and Roman Catholic Church are allowed to sit on Sutton Council's children, family and education committee but are only allowed to take part in debates concerning educational matters.
Catholic representative Andrew Theobald and Anglican representative Peter Gowlland have left the last three meetings in protest at not being allowed to take part in debates concerning safeguarding children - the council's responsibility to identify and look after vulnerable young people.
The pair say safeguarding is an educational issue as it involves schools and are supported in this by the head of the Sutton Teachers Association.
But Councillor David Callaghan, chairman of the committee disagrees.
The impasse continued at the most recent committee meeting on Thursday, November 15, with the pair walking out of the meeting and demanding their departure be minuted as a protest.
As he walked out Mr Theobald said: "We dispute what you're doing - we withdraw under protest. We have a right to be here. As far as we're concerned safeguarding is an education matter."
The pair also disputed how their departure from previous meetings was minuted. In the minutes of the last meeting it says they left "at the close of discussion on education matters".
Mr Theobald asked that it be changed to say they left the meeting "at this point" to emphasise his view that educational matters continued after they left.
Coun Callaghan refused and said: "The reason you're asked to stand down is because we have reached the end of educational matters, the educational matters have been discussed. The position of the local authority is that the diocese representatives should stand down. I'm not sure there's a huge difference between 'at this point' and 'at the end of educational matters'. You're asking us to record that you've left the meeting under protest but you've not been asked to join the meeting."
Sue Smith head of the Sutton Teachers Association, asked Coun Callaghan: "What I'm interested in is your [safeguarding] board. You have school representatives, you have head teachers and from primary schools and secondary schools. I know you have the view that this is nothing to do with education but education is surely part of it."
Coun Callaghan said Mrs Smith remarks were a "misrepresentation" of his view.