LONDON (AP) — The Church of England has much explaining to do following its failure to vote to allow women to serve as bishops, its leader said Wednesday — and politicians from the prime minister downward are already demanding action or answers.

One legislator even suggested there might be an issue under anti-discrimination laws.

The governing General Synod blocked the change as the vote among lay members on Tuesday fell short of the required two-thirds majority. Bishops and clergy, in separate votes, overwhelmingly backed the proposal.

Speaking to the synod a day after the vote, Archbishop of Canterbury Rowan Williams said any church member who thought there was an easy solution to the impasse between traditionalists and proponents of female bishops was being unrealistic.

"Yesterday did nothing to make polarization in our church less likely," said Williams, who had long supported the proposed change.

"We have, to put it very bluntly, a lot of explaining to do," he added.

Speaking in the House of Commons, Prime Minister David Cameron urged the church to resolve the schism and swiftly approve female bishops.

"I'm very clear the time is right for women bishops, it was right many years ago," Cameron said.

"They need to get on with it, as it were, and get with the program. But you do have to respect the individual institutions and the way they work, while giving them a sharp prod."

Labour Party lawmaker Diana Johnson asked for a statement from the church's representative explaining "what this means in terms of the continuing discrimination of having only men eligible to sit in the House of Lords as bishops."

John Bercow, the speaker of the House, noted that there were "very strong voices" in favor of women bishops among legislators.

He suggested that Johnson approach Maria Miller, the government's minister for women and equalities, to see whether she "has any responsibilities in relation to this matter."

More than 100 members of the General Synod spoke in Tuesday's debate, largely repeating arguments which have become familiar in the 18 years since the church began ordaining women as priests.

Williams, who had campaigned for the change, said that much of the prolonged debate is "not intelligible to our larger society."

John Sentamu, the archbishop of York, said he was confident that women would become bishops in his lifetime.

"The principle has already been accepted by the General Synod, it has already been accepted by all the dioceses," Sentamu, 63, said in a BBC radio interview.

"So what we need to do is find the legislation: 99.9 percent of the legislation is there, it's this little business of provision for those who are opposed," Sentamu said.