The leadership duo at the top of the CBI was involved in a bizarre exchange on a call with dozens of leading members on Friday as the business lobbying group fights for survival.

Sky News understands that Rain Newton-Smith, the new CBI director-general, highlighted a dearth of female questioners during a briefing she jointly hosted with Brian McBride, its president.

According to one account, Ms Newton-Smith highlighted at the end of the question and answer session that Mr McBride had yet to select a female contributor.

The session was extended to include questions from two women, one of whom is said to have pointed out the gender imbalance.

A source close to the CBI said the questions had been picked in order of registration.

Nevertheless, the exchange between Ms Newton-Smith and Mr McBride was interpreted by one listener as “awkward” and “embarrassing given the context”.

The call with trade association representatives on Friday morning was part of an effort by the CBI’s leadership to convince tens of thousands of members to vote in favour of a confidence motion at an extraordinary general meeting next Tuesday.

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The UK’s biggest business group has been left on the brink of extinction by its handling of a sexual misconduct scandal which was preceded by the ousting of its former D-G, Tony Danker, over unrelated claims about his behaviour.

Earlier this week, the CBI published a prospectus setting out its reform agenda, which included a string of board changes and the creation of several new committees.

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However, many members have expressed dissatisfaction with the document, saying it had left them underwhelmed and that it had no financial or strategic plan for the CBI’s future.

To illustrate the apathy felt by many corporate members, PricewaterhouseCoopers, the UK’s biggest accountancy firm, does not plan to register a vote in next week’s ballot, according to insiders.

Sky News revealed this week that the board of the CBI had drafted in lawyers to prepare for a prospective insolvency filing ahead of the crunch vote.

An adverse outcome from a vote at next week’s extraordinary general meeting would leave directors with little choice but to begin a process to wind it up.

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Next week’s EGM will take place on a ‘one member, one vote’ basis, with the CBI requiring a majority of votes cast in favour of a resolution expressing confidence in its ability to deliver a new mandate.

The CBI has already been hit financially by the cancellation of membership subscriptions by dozens of blue-chip members, including Aviva and the John Lewis Partnership.

Numerous others have suspended their engagement, while both the government and Labour have said they will not interact with the CBI while a police investigation into alleged rapes takes place.

In April, the UK’s biggest business group suspended most of its activities pending the outcome of a root-and-branch review.

“Without a mandate from you, we have no future,” Ms Newton-Smith has told members.

“With a general election looming, the voice of business urgently needs to be heard.

The CBI declined to comment on Friday.