The president of the CBI has admitted he does not know if it can win back trust while setting out how it plans to bolster its culture amid the sexual misconduct scandal engulfing the business lobby group.

The UK’s most prominent business lobby group, the Confederation of British Industry, has won support from its remaining members to continue speaking for firms after vowing to reform its culture and governance.

But in a sign of the continued turmoil it faces, Rishi Sunak declined to say whether the government would resume links with the group, saying the CBI “have their issue so they need to work through”.

The CBI, which has been in crisis since the Guardian first reported allegations of sexual misconduct, said 93% of members voted in favour of its plans for change in a crunch vote of confidence, while 7% cast their votes against the proposals set out by management.

Rain Newton-Smith, who replaced Tony Danker as CBI director general after he was dismissed following separate complaints about his conduct, said: “After an incredibly tough period, I’m deeply grateful for the faith shown in us by our members.”

She added that the CBI was committed to change.

“Let me be clear, we have listened, we have acted, and we will leave no stone unturned to be the best voice for business inside and out,” Newton-Smith said.

There were 371 votes in total, with 23 abstentions and votes withheld, but the CBI did not disclose the turnout or the overall number of members. It is understood to have had about 1,500 direct members before the recent turmoil. However, after allegations surfaced, over 20 major companies and trade associations, including the insurer Aviva, NatWest bank, John Lewis and BMW publicly left the lobby group in protest.

Speaking to reporters on his plane en route to Washington, Sunak said he had not seen details of the vote, and would thus not commit to government fully re-engaging with the CBI, saying it liaised with numerous business groups.

“Matters at the CBI are for the CBI and for its members to work through,” he said. “I haven’t seen the details. I’m sure they will work through that with their members. For out part, we continue to engage with businesses individually and business groups.”

Pressed again on whether ministers would reconnect with the CBI, the prime minister said: “We work and engage with lots of different business groups and businesses individually, but the CBI have their issues which they need to work through, which we should just let them do.”

Labour also confirmed it would also not re-engage with the group.

On Tuesday, it emerged that several more FTSE 100 businesses had quit the CBI, including Tesco, BP and National Grid. A Tesco source told the Guardian: “We paused in April. We took some time to reflect on it and terminated our membership on Friday.”

A spokesperson for the CBI declined to say how many businesses it now represents or if any members had asked to rejoin.

The CBI is battling to regain trust after the government and the Labour party suspended further engagement, and meetings between the group and civil servants were paused pending the outcome of various investigations.

Some of the allegations, which include sexual harassment, sexual assault and rape, are being investigated by the City of London police. The president of the CBI admitted it had failed to filter out “culturally toxic people” following an independent investigation by law firm Fox Williams. Some managers were suspended and have now left the organisation.

In its bid to relaunch itself, the CBI said that it had problems to address, rather than a pervasive toxic culture after a second review by a consultancy, Principia. The consultancy did find persistent failings at the body, however.

“Both businesses and government will now want to see clear evidence that the CBI is delivering on its promise to change,” said Ann Francke, chief executive of the Chartered Management Institute. “A mandate from the members is not enough, on its own, for the CBI to believe it can draw a line under the events of the last six months and move on.”

Members were asked to vote in response to the question: “Do the changes we have made − and the commitments we have set out − to reform our governance, culture, and purpose give you the confidence you need to support the CBI?”

A significant number of employees at the lobby group still expect to be faced with redundancy even with the backing of some remaining members, several told the Guardian. Managers told staff last week it would need to slash a third of its wage bill.

Danker was dismissed in April after separate allegations were made about his own conduct. Danker said he felt he had been made the “fall guy” for the wider crisis faced by the organisation. After his dismissal, Danker also said he was “truly sorry” for making some colleagues “feel uncomfortable”.

One executive, who attended the CBI meeting, said: “While they may have retained the confidence of their smaller members, they have lost the credibility with the very politicians their members need them to influence. Ahead of such an important election, it is hard to see them regain their legitimacy.”

Large businesses Shell, Diageo, SSE and Asda – which had all paused their engagement with the CBI – said they had voted in support of management.

One gap that appears to be left in an organisation meant to speak for British business is finance and professional services, a key chunk of the UK’s services-heavy economy.

Insurance industry body the British Insurance Brokers’ Association, which represents 1,800 insurance brokers, the Association of British Insurers and Lloyd’s of London had already quit the lobby group. Alongside Aviva and NatWest, Mastercard and the insurer Zurich have also quit.

The so-called “big four” audit and accountancy firms also appear to have abandoned the body. PwC is understood not to have taken part in Tuesday’s vote, while KPMG let its membership lapse before it was held. EY and Deloitte had already terminated theirs.

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CBI survives confidence vote after sexual misconduct allegations

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