The chair of the lay house of the Church of England's General Synod, which controversially rejected legislation to create female bishops last month, is to face a vote of no confidence amid accusations that his stance on the issue "directly undermined" the next archbishop of Canterbury and caused the church "reputational damage".

Although the legislation was supported by the houses of clergy and bishops, it was eventually defeated by the house of laity, leading one bishop to warn that the church was in danger of becoming "a national embarrassment".

The house's chair, Dr Philip Giddings, has now been accused of compromising the authority of Justin Welby, who will succeed Rowan Williams as leader of the Church of England next year, and who, like Williams, favours the introduction of female bishops.

During a speech to the synod that came directly after Welby urged its members to vote in favour of the measure, Giddings said it would be "unwise" to press ahead with a measure that "a significant minority of our church" were unable to accept.

He added: "We have been told that we have debated these matters long enough. Long enough perhaps for those who are in the majority and can impose their will, but not long enough to gain the consent of those who are opposed and whose consent is essential if we are to remain a united and growing church committed to mission."

Giddings, one of the most powerful lay members of the church, is also the convenor of the conservative evangelical Anglican Mainstream network, which was founded to oppose the appointment of Jeffrey John, a gay priest, as the suffragan bishop of Reading in 2003.

His position on female bishops has prompted one member of the house of laity, Canon Stephen Barney, to propose a motion of no confidence, which will be debated at an extraordinary meeting on 18 January.

In a statement issued on Wednesday, Barney said Giddings's speech had "directly undermined what the archbishop elect had said" and contradicted "the views of the house of bishops as a whole".

He also said the speech had been instrumental in convincing some of the undecided members of the house to vote against the measure.

Barney added: "I believe the speech was therefore a significant contributor to the reputational damage the Church of England is already suffering at the hands of the press, which is also manifest in the comments of the prime minister, the emerging reports of withdrawal of financial support, the angry reaction of church members and the disbelief and ridicule expressed by many of our secular friends, all of which I believe will damage the mission of our church."

Details of the debate emerged as the church announced the composition of a new house of bishops working group charged with helping it develop new legislative proposals on the issue of female bishops.

Its members, who will be drawn from all three houses of the General Synod, include Giddings. The group, which will meet twice next month, has been asked "to arrange facilitated discussions in February with a wide range of people of a variety of views".

The house of bishops is due to bring the new proposals to the synod in July.