A bishop is facing calls for an investigation into whether he has given “just cause for scandal” after the breakdown of his marriage.

The Bishop of St David’s, the Right Rev Carl Cooper, 47, announced two weeks ago that he and his wife were separating after 25 years. In a letter to all clergy in his Welsh diocese he said that no one else was involved “on either side”.

Two of his own vicars have called for the inquiry after rumours linking him to the Rev Mandy Williams-Potter, the diocesan communications officer, suggested that he may have been less than forthcoming about his private life. The vicars have written to other clergy in the diocese urging them to join in petitioning the Archbishop of Wales for an investigation.

The Rev Dr Will Strange, Vicar of St Peter’s, Carmarthen, and the Rev Peter Jones, Vicar of Llangennech, Llanelli, said: “We write this letter with a heavy heart. It is an appeal to you to join in petitioning the Archbishop and the Bench of Bishops to institute a process under Chapter XI of the Constitution.

“The aim of this process would be to establish the facts surrounding the Bishop’s current situation and to take whatever action, if any, proves necessary. This is not a welcome responsibility for any of us but we are convinced that if the Church has established a procedure for such situations it should apply equally to all clergy of whatever rank.”

They added: “Signing this letter is not in any sense to prejudge what the process may determine and decide. It is not even to assume there is anything untoward to discover. But it is an opportunity to say that where there is a perception of ‘conduct giving just cause for scandal and offence’ the circumstances should be subject to the Church’s investigative and disciplinary procedure.

“For us as clergy to do any less would be to acquiesce in a situation which is causing distress across the diocese to many, both lay and ordained.”

Dr Strange and Mr Jones said yesterday that they had received a mixed response. “We are not making any allegations or claims or trying to cause trouble for the Bishop,” Dr Strange said. “It is a very difficult situation and we are trying to find the right way to deal with it.”

The Bishop issued the statement last month saying that he and his wife, Joy, were separating. “Sadly and tragically we have decided to separate,” he wrote. “There is no one else involved on either side. We are committed to an ongoing, amicable relationship of mutual care and support.

“The challenges in our marriage are personal and shall remain private for our own sakes and that of our family and loved ones.”

Mrs Williams-Potter, who is married to a teacher, said yesterday that she and the bishop were “just good friends”. She added: “I know about the rumours but I don’t know where they have come from and there is nothing in them. Obviously someone has been spreading this information but I don’t know who it could be. I’m married and my husband and I are together.”

A spokeswoman for the Archbishop of Wales, Dr Barry Morgan, said: “The Church’s policy is that all clergy have to be above suspicion. Any allegations of misconduct or inappropriate conduct are investigated.”

The Archbishop said that he was “enormously sad” to hear of the breakdown of the Coopers’ marriage. “My thoughts and prayers are with Bishop Carl and Joy as they go through this difficult time,” he said.

Bishop Cooper, who has spoken out against the war in Iraq, child poverty and super-casinos since his appointment in 2002, was carrying out his duties yesterday. He declined to elaborate on the statement announcing the end of his marriage. The couple have three children aged 17 to 22.