This is an example of the "busy governor" problem at its worst. I'm all for opinion surveys, provided they are well structured and properly managed. And listening is, of course, part of the governor's role, especially elected ones, since they may on occasion need to provide colleagues with an idea of feeling in the "constituency". But individuals should never be left to beaver away on their own with clipboards and leading questions. It is for the governing body as a whole to decide whether and when to use surveys.
I'm surprised a teacher or support staff governor has not reacted to this by now, since it is an issue for the governing body. I don't think the head is the right person to complain to, however; it isn't for the head to tell governors how to behave. The proper thing is to have a word with the chair. The governing body must provide its own discipline, and the chair is the obvious source of this in the first instance.
In the unlikely event of this problem not being solved without a fuss, there is a procedure for a governing body to remove a co-opted governor, which you will find laid down in your Guide to the Law. (Parent and teacher governors are not covered because they are elected, and foundation and local authority governors can only be removed by their appointing body.) It takes place over two meetings and requires a larger than usual quorum. The person must know what is alleged and have a chance to reply, accompanied by a friend if he or she wants. I hope your case won't require such drastic measures.
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