Question

Can a parish council pass a motion which overrides an existing Standing Order, without varying the Standing Order?

Answer 1

Yes, provided the standing order to be overriden is not demanded by the law.  You'll probably find that your standing orders contain a list of motions that can be moved without notice.  One of them (in bold because it is part of the legislation) probably says something like "To suspend any standing order except those which are mandatory by law. "

So the usual procedure is to move a motion to suspend the standing order that is in the way of what is to be done, and then deal with the motion in question.  That procedure doesn't permanently affect the standing orders, just temporarily sets one or more aside for a specific purpose.