Speaking at prime minister's questions, David Cameron expresses his disappointment at the vote by the Church of England's General Synod Press Association

David Cameron has urged the Church of England to "get on with it" and reverse its decision to reject female bishops.

The prime minister told MPs that the church needed "to get with the programme", adding: "You do have to respect the individual institutions and the way they work, while giving them a sharp prod."

Later the PM's spokesman said Cameron could not understand why the review of the decision should take years, as the Church of England has said.

His remarks made at prime minister's question time are the clearest sign yet that he does not want to leave the issue alone, even if he is not going to change the law to make the church subject to the European court of human rights.

Cameron said he was "very sad" about the result. "On a personal basis I'm a strong supporter of women bishops. I'm very sad about the way the vote went yesterday and I'm particularly sad for the archbishop of Canterbury, Rowan Williams, because I know he saw this as a major campaign that he wanted to achieve at the end of his excellent tenure of that office. 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 it needed to take."

The Speaker, John Bercow, also urged backbenchers to see if they could ask the equalities minister, Maria Miller, to come to the Commons and make a statement, so giving MPs an opportunity to express their dismay at the decision of the church. The prime minister's spokesman added that it was right for parliament to express a view.

Rowan Williams earlier told the General Synod that the Church of England had "a lot of explaining to do" after its rejection of legislation that would have allowed women to become bishops.

In a strongly worded speech on Wednesday, Williams warned that the failure of the vote in the house of laity on Tuesday had made the church's governing body appear "wilfully blind" to the 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. Worse than that, it seems as if we are wilfully blind to some of the trends and priorities of that wider society."

Justin Welby, the bishop of Durham, who succeeds Williams as archbishop next year, has insisted that women will eventually be ordained as bishops despite the change being voted down.

He said the General Synod had "overwhelmingly" backed the idea, although it did not receive the two-thirds majority needed among lay members.

Welby said he agreed with comments by the archbishop of York, John Sentamu. "Sentamu has said there will be women bishops and I agree with him," he told the Press Association.

"The church has voted overwhelmingly in favour of the principle. It is a question of finding a way that there is a real consensus that this is the right way forward.

"That is going to take some time, some care, and some prudence."

Asked whether he was determined to push the issue, Welby, who had earlier tweeted that Tuesday was a "very grim day", said: "I'm going to listen to all the other bishops and we will talk together and decide together."

He was speaking after attending a parliamentary hearing at which he made a wry joke about the female bishops vote as he questioned the chancellor of the exchequer, George Osborne.

The bishop of Durham sits on the parliamentary commission on banking standards, which is carrying out an inquiry into the culture and practices of the financial services industry.

After Osborne mentioned "lay" members of banking boards while giving evidence on Wednesday, the bishop provoked laughter by saying: "Thank you, Chancellor, that when you said 'lay people', you didn't say 'male lay people', [given] the present situation I'm facing."

The chancellor said: "Can I congratulate you on your …"

But before he could finish his sentence, the bishop again prompted laughter by saying: "I'm not sure you can."

Osborne told him: "I thought I had a difficult job but, over the last 48 hours, I have seen you have got a much more difficult job and I wish you very well personally with that."

Sources close to the culture secretary, Maria Miller, who is also equalities minister, issued strongly worded criticism after the vote on Tuesday night to open up the episcopate to female clerics fell short of the necessary two-thirds majority by six votes.

But it was stressed by No 10 that this displeasure would not extend to direct intervention in the internal workings of the Church of England.

Allies of Miller said: "Whilst this is a matter for the church, it is very disappointing … as we seek to help women fulfil their potential throughout society this ruling would suggest the church is at the very least behind the times."

Philip Hammond, the defence secretary, said the Church of England must resolve the issue of female bishops: "Otherwise it's going to increasingly find itself marginalised."

The Labour MP and active Christian Chris Bryant has suggested he will introduce legislation that would require the CofE to be compliant with UK equality laws.

He said he feared the church may have died as a national institution as a result of the vote.

Another former minister, Ben Bradshaw, claimed the church was "being held hostage" by evangelicals and conservatives. "This means the church is being held hostage by an unholy and unrepresentative alliance of conservative evangelicals and conservative Catholics," Bradshaw said.

The church has an exemption from equalities and employment legislation allowing it to disbar women from the episcopate. If that immunity was removed, it would be possible for women to sue the CofE for discrimination.

It would not be possible for such legislation to be pushed through parliament without the support of the government, although MPs such as Bryant could introduce 10-minute rule bills, or a private member's bill.

Senior Liberal Democrats, including the chief whip, Alistair Carmichael, questioned whether bishops should be allowed to stay in the House of Lords if they were going to remain male-only appointments.