The chairman of BBC’s board, Richard Sharp, resigned on Friday after an investigation concluded that he failed to disclose his involvement in arranging a nearly $1 million loan for the former prime minister, Boris Johnson.

Mr. Sharp said in a statement, shortly before the report was released, that the omission was “inadvertent and not material” but that he had decided to step down from the broadcaster’s board to “prioritize the interests of the BBC.”

His departure deepens the turmoil that has enveloped Britain’s public broadcaster in recent months over accusations of political bias and questions about its close ties to Britain’s Conservative government. The BBC’s role has come under relentless fire in an era of polarized politics and freewheeling social media.

It suspended its most prominent on-air personality, Gary Lineker, last month after he posted a tweet likening the government’s immigration policy to that of Germany in the 1930s. That triggered a walkout of the BBC’s sports staff and forced it to broadcast “Match of the Day,” its flagship weekly soccer program, without commentary.

The BBC settled the dispute with Mr. Lineker by vowing to review its policies governing the use of social media by its on-air personalities. But the suspension threw a harsh spotlight on Mr. Sharp because he refused to step down from his job, even though he was undergoing an investigation for his role in the loan to Mr. Johnson.

Mr. Sharp’s compromised position also meant he could not defend the BBC at a time when it was coming under fierce criticism from all sides — for the haphazard enforcement of its social media guidelines, as well as for the settlement with Mr. Lineker, which many Conservatives criticized as a capitulation.

The episode prompted calls by the opposition Labour Party for Mr. Sharp’s resignation. The current prime minister, Rishi Sunak, appeared to distance himself from Mr. Sharp, even though the two had once worked together at Goldman Sachs, where Mr. Sunak and Mr. Sharp had both been bankers.

Mr. Sharp, a major donor to the Conservative Party, said he regretted not raising the issue of the loan with an appointments panel before he took the post of chairman. The report found that he helped facilitate a loan guarantee worth 800,000 pounds, or $996,000, for Mr. Johnson.

“I wish, with the benefit of hindsight, this potential perceived conflict of interest was something I had considered to mention,” he said in his statement. “I would like once again to apologize for that oversight — inadvertent though it was — and for the distraction these events have caused the BBC.”

The BBC’s director general, Tim Davie, who is himself under pressure for his role in the dispute with Mr. Lineker, credited Mr. Sharp “for his service to the BBC and the drive and intellect he brought to his time as chairman.”

For all the criticism of Mr. Sharp’s role in the loan to Mr. Johnson, media analysts said he deserved credit for negotiating a deal with the government in January 2022 that secured the BBC’s license fee, the main source of its funding, for the next six years.

“Mr. Sharp was a most effective chair at the most delicate time in its history and ensured its future,” said Claire Enders, a London-based media researcher and the founder of Enders Analysis. She said the deal was a “miracle,” given the hostility many in the government felt toward the BBC.