The Very Rev Bob Key was attending a meeting of the Diocese of Winchester, which like all other dioceses in the UK had been asked to consider the move before a decision by the General Synod in July.
The change, which needed a majority to go through, was passed by two votes. However, Mr Key said that more work needed to be done on the legislation if he were to support it next year.
His concerns relate not to the principle of women becoming Bishops, but to the safeguards in place to protect congregations or clergy who feel for whatever reason that they cannot accept a female Bishop.
