Kemi Badenoch, the business secretary, has turned down an invitation to address the CBI’s annual conference, dealing a blow to the business lobbying group’s efforts to rebuild its reputation.

Sky News understands that Ms Badenoch’s officials have informed the CBI that diary clashes in the run-up to next month’s autumn statement will prevent her from addressing the summit in central London.

Her decision leaves the CBI without a confirmed senior government minister as a speaker with less than a month to go until the event takes place.

The CBI has secured funding to ensure its short-term survival after a torrid six-month period in which it teetered on the brink of collapse.

A sexual misconduct crisis, which included several rape allegations against former employees, triggered an exodus of corporate members including Aviva and John Lewis Partnership.

Tony Danker, its director-general – who was accused of inappropriate behaviour but had nothing to do with the more serious allegations – stepped down in April weeks after being suspended.

The CBI briefly entertained talks about a merger with Make UK, the manufacturers’ body, but these have now been curtailed.

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Mr Danker’s successor, Rain Newton-Smith, met the chancellor, Jeremy Hunt, last week – the first bilateral meeting between the CBI and a senior minister since the crisis.

The CBI declined to comment specifically on Ms Badenoch’s invitation, but said last month of its conference: “We are bringing businesses together for an event later this year that aims to set the economic agenda ahead of a pivotal election for the country.”

Established by royal charter in 1965, the CBI’s financial crisis has forced it to slash jobs and close overseas offices.