A VERY interesting question. When I was asked by a county LEA to write a booklet for LEA governors I couldn't find guidance anywhere, so was left with my own thoughts and reasonings. You must take this reply in that spirit.
No governor is a delegate. Many governors besides LEA ones - parents and teachers especially - have a representative role, which means they have to try to understand and pass on the views of those who put them there. But in deciding how to act, they must be guided only by the needs of the school as they see them.
So LEA representatives should not feel constrained by the LEA's policies, if they seem to be contrary to the school's interest.
I have been lucky to work with party nominees who ave been courageous in following their consciences, and I should find it hard to accept that any such governor did not put the school first when within its walls.
I am supported in this interpretation by two legal cases involving attempts by an LEA and a foundation to remove governors they had nominated. In one case it was for not voting according to the policies of the appointing body on important school issues. In the other it was an attempt to replace a party nominee when control of the council changed.
The judgments included some useful legal opinions, namely that an appointed governor could be removed if she had ceased to be generally representative of the appointing body.
But such a governor could not be removed for having taken an independent line in the discussion and decisions of the governing body.
It is important that a school has confidence in governors to put the needs of the school first. Otherwise, the representation of the school's providers (LEA or voluntary body) will be brought into disrepute, a pity when LEAs generally are beginning to adopt more liberal appointing policies and seeking nominees of quality both from inside and outside the political parties.