Backed by politicians of all stripes, prime minister urges Church of England to 'get with the programme' and reconsider decision

The stage is set for a clash of wills between church and state after David Cameron, backed by politicians from all sides, openly urged the Church of England to quickly revisit its decision to reject the ordination of female bishops.

Church rules state that the measure cannot be brought back before the General Synod "in the same form" during the current term, which ends in 2015. But the prime minister's spokesman said the government did not understand this timetable.

A saddened Cameron told MPs: "I am very clear that the time is right for women bishops; it was right many years ago. The church needs to get on with it and get with the programme."

Parliament had to "respect individual institutions and how they work, while giving them a sharp prod", he added. "I think it's important for the Church of England to be a modern church, in touch with society as it is today, and this was a key step they needed to take."

His remarks were designed to put pressure on the new church leadership to return to the issue more quickly than a strict interpretation of the church's rules allows.

The shadow equalities minister, Yvette Cooper, told the church: "It can't just let this lie for the next five years." In a sign of the anxiety across parliament, the Speaker, John Bercow, urged backbench MPs to ask the equalities minister, Maria Miller, to make a formal statement to the Commons on Thursday .

The government argues that the narrowness of the vote justified revisiting the issue quickly, and for ministers to step up the public pressure. Ministers were reluctant to join calls by some angry MPs to force the church to rethink by removing its protections from equalities legislation or by acting to debar bishops from the House of Lords. But, in a sign of the exasperation of leading politicians with the church decision, the normally measured defence secretary, Philip Hammond, warned that the church was no longer in the mainstream of Anglican thought.

"It's not just … the ordination of women but a series of big, divisive issues which the church has to resolve. It has to heal. It has to find a way forward. Otherwise, it is going to increasingly find itself marginalised. It's going to find members of the church with strong views on one side or the other of these arguments, I think, increasingly [will] be attracted to splinter groups and splinter churches.

"So it is essential that the Church of England finds a way of recovering that middle ground and becoming the mainstream of Anglican thought in this country again."

Frank Field, a leading Christian Labour MP, said he would present a private member's bill to parliament on Thursday calling for the cancellation of the church's exemptions from equality legislation. "When we gave exemptions under the Sex Discrimination Act we were assured that the church didn't want to discriminate and that it would bring forward measures to eliminate such discrimination," he said.

But Tuesday's vote had made clear that that had not happened. "Parliament made a gracious act under a misapprehension," he said.

Chris Bryant, a Labour MP and a former Anglican priest, said the failure of the vote had caused many to call into question the future of the 26 bishops in the House of Lords.

Reflecting an awareness in the church's leadership of how much damage the crisis could do, the outgoing archbishop of Canterbury warned the synod that it had to move forward as quickly as possibly with finding a way of getting women into the episcopate in order to avoid losing even more credibility than it already had. "Every day that we fail to resolve this to our satisfaction …is a day when our credibility in the public eye is likely to diminish," said Rowan Williams, in a strongly worded speech. The failure of the legislation had left the church looking "willfully blind" to the trends and priorities of secular society.

"We have – to put it very bluntly – a lot of explaining to do," he said. "Whatever the motivations for voting yesterday … the fact remains that a great deal of this discussion is not intelligible to our wider society."

As the campaigners and the wider church community continued to reel from Tuesday's dramatic outcome, Williams said the church's governing body could not "afford to hang about".

"After all the effort that's gone into this process over the last few years, after the intense frustration that has been experienced in recent years … it would be tempting to conclude that it's too difficult, that perhaps the issue should be parked for a while," he said. "I do not believe that is possible because of … the sense of credibility in the wider society."

Williams, for whom the failure of the vote was a bitter disappointment and a disastrous end to a fraught decade in Lambeth Palace, was given two standing ovations in an emotional farewell to the synod. The man who is to replace him, Justin Welby, joined the archbishop of York, John Sentamu, in insisting there would soon be female bishops in the Church of England. The church has voted overwhelmingly in favour of the principle," he said. "It is a question of finding … a real consensus that this is the right way forward. That is going to take some time, some care and some prudence."