The former prince was arrested on suspicion of misconduct in public office on Thursday morning, UK time, and released under investigation in the evening by police over his ties to convicted sex offender Jeffrey Epstein.
Giuffre, who died by suicide in 2025, alleged she was forced to have sex three times with Andrew, including when she was 17, and also during an orgy, after she was trafficked by Epstein.
Andrew has always denied the claims.
Charles stripped his younger brother of his prince and Duke of York titles in 2025 amid the scandal surrounding Andrew's friendship with the late financier.
In an interview with the BBC, Sky Roberts, Giuffre's brother, praised the King for his response following Andrew's arrest, adding: "We have yet to see that from our own government here."
Roberts said that although Andrew's arrest "may not be a direct correlation to what the sexual assault allegations may be", it was "a win" for his sister and other survivors and "a very good start to opening an investigation".
"I think to hear the King come out and acknowledge the fact that there needs to be an investigation, the law should be followed, like it should be followed for anybody that should be held to this type of investigation," Robert said.
"And if it is found that he indeed did share secret information from his own government, I mean, that's a crime that's punishable by life.
"We would ask that he holds them to the highest extent of the law, even though it is his brother.
"So I commend the King. I say thank you to the King and to the royal family for standing behind survivors, but also just standing behind their people to say, it doesn't matter ... your wealth or your power, you don't have a different set of laws for you that don't apply to other people."
Speaking on the same program, Giuffre's sister-in-law Amanda Roberts said her family believed Andrew's arrest was the "breadcrumb to the larger dinner" regarding the investigation.
"There's still this underlying issue of survivors not getting their day in court and not seeing judicial, legal action," she said.
"However, we still are true in believing that it is the breadcrumb to the larger dinner.
"And so we are hopeful that this investigation now starts to open up that further probe into the sexual assault allegations, into the child trafficking. So it still is a win."
Amanda Roberts said Giuffre's family was hit by a "wave of emotions" upon hearing the news of former prince Andrew's arrest.
"It was 3am our time when we got the news and a bit of a shock, like, hits you in that moment and I think we celebrated in that moment and we were just struck.
"And then the wave of emotions hits you because, usually we can call her and scream with her on the phone, and jump up and down with her, and just get to tell her how proud we are of her, and her tenacity and her courage.
"And if it had not been for Virginia, none of this would have been uncovered. None of this would have happened."
In 2022, Mountbatten-Windsor paid millions to settle a civil sexual assault case with Giuffre despite insisting he had never met her.
Her memoir, Nobody's Girl, was published posthumously in October and gives her account of being trafficked by Epstein and the three alleged sexual encounters with the then-prince.
He was stripped of his titles in the wake of its release.
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