If you're hoping for a procedure to oust a councillor, I'm afraid you're out of luck! A councillor becomes disqualified only for limited reasons. The main ones are failure to attend meetings without reason for six months, becoming bankrupt or being sentenced to at least three months imprisonment (even if suspended). They can also become disqualified in relation to corrupt or illegal practices, or by becoming a paid officer of the council.
However, citizens do have the right to call a parish meeting, which requires 10 signatures. A parish meeting can be called to discuss any local matter, and can pass resolutions. These are not binding in all but a few specific cases, but will have some impact as expressing local feeling.
In the short run, the only effective way is public pressure leading to resignation. Many people are not so thick skinned as to ignore being castigated by their fellow citizens. In the longer run, the solution is for other candidates to stand at the periodic elections. In any case, it is always a good thing for there to be new blood coming forward to seek election to a council.