The Jeffrey Epstein scandal has ripped through the highest levels of Britain, prompting the firings of two top officials and a rupture in the royal family. Now it looms over the state visit of King Charles III and Queen Camilla.

Mr. Epstein, the convicted sex offender, cultivated ties with political and business elites on multiple continents, including with Andrew Mountbatten-Windsor, the king’s brother. Mr. Mountbatten-Windsor was stripped of his titles over his connections to Mr. Epstein and was arrested this year over accusations of misconduct in public office, after reports that he may have shared confidential information with Mr. Epstein while serving as a British trade envoy. He has denied wrongdoing and has not been charged.

After his brother’s arrest, the king made a rare and direct public statement expressing support for an investigation. Since then, he has limited his public comments on the issue.

The king and queen will not meet with Mr. Epstein’s victims while in the United States, despite a request from Representative Ro Khanna, Democrat of California. Lawyers representing Charles and Camilla said that they were unable to do so because of “ongoing police inquiries” in Britain.

Family members of Virginia Giuffre, a woman who said that Mr. Epstein had trafficked her to Britain and forced her to have sex with Mr. Mountbatten-Windsor in 2001, expressed their frustration. “This is a missed opportunity,” Sky Roberts, Ms. Giuffre’s brother, told Britain’s Sky News.

Ms. Giuffre died by suicide last year before her memoir was published. Over the weekend, her family held a vigil in Washington to observe a year since her death.

“It means something to look into a survivor’s eyes and say: ‘I promise to give you a fair and thorough investigation in this, and that does not matter if it’s my brother or if it’s other perpetrators out there. I, the King of England, stand with survivors,’” Mr. Roberts added.

The Epstein scandal has also unraveled the career of Peter Mandelson, who was fired from his post as Britain’s ambassador to the United States last year after a batch of files showed the depth of his friendship with Mr. Epstein.

Mr. Mandelson was arrested this year over accusations that he had passed on confidential government information to Mr. Epstein in the late 2000s.

Mr. Mandelson is not accused of sexual misconduct. He remains under investigation but has not been charged with a crime and has denied any criminal wrongdoing.

Prime Minister Keir Starmer of Britain also fired Olly Robbins, the top civil servant in the Foreign Office, after it emerged that the department did not tell ministers that Mr. Mandelson had failed top-level vetting checks before he became ambassador. On Tuesday, during the royal visit, British lawmakers back in London heard testimony from other officials over the Mandelson case.