The Church of England faces growing pressure to rip up its rulebook to allow the ordination of women bishops.
Culture secretary and minister for Equalities Maria Miller and former Archbishop of Canterbury Lord Carey of Clifton have added their voices to those demanding urgent reformation of the church's internal policies.
Allowing women to become bishops was narrowly defeated in a vote by the church's governing body, the General Synod, on Tuesday, despite overwhelming approval from many of its members.
Female bishops were approved by the majority of dioceses, bishops and clergy, but were rejected by the laity.
Miller told The Guardian it was "extraordinary" and "very disappointing" that the vote had failed, and urged the church to examine its "procedures and processes" and why its decision had not reflected the views of its members.
She told the newspaper: "If you're going to tackle the problem, I think the church needs to be answering some of the questions as to why their system works the way it does, and are they really happy that it's reflective of the views of their membership."
She added: "I think it's extraordinary that the church seems to have ended up in a situation where a vote that was taken doesn't seem to be reflective of the overwhelming views of the members of the church."
Calling for the church to reconsider the issue, Miller said: "Obviously, it's for the Church of England to run its own procedures and processes, but I really hope that they have heard, loud and clear, the strength of feeling on this, and that it acts quickly."
Lord Carey, who oversaw the ordination of women priests during his tenure as Archbishop of Canterbury, also demanded change, labelling the vote "appalling", The Times said.
He called for a way to speed up the General Synod's reconsidering of women bishops - which under current church legislation cannot be brought back in the same form until 2015.
He told The Times: "We are 19 years into the priesthood of women. They are doing a wonderful job. They should get their chance now. I remain very pleased we ordained women priests in my time. It is time to move on and ordain women to the episcopate. Where there is a will, there is a way.
"The important thing is to find a way to get the desired outcome that the majority want."
Justin Welby, the Bishop of Durham, who will take over from Dr Rowan Williams as the Archbishop of Canterbury next year, will support a meeting with MPs and Lords to discuss the crisis within the church, The Guardian said.