The historic statement from Buckingham Palace stripping Andrew Mountbatten Windsor of his title is an “acknowledgment” that something happened to the late Virginia Giuffre, her family has told the Guardian.

In its announcement on Thursday, the palace said Andrew Mountbatten Windsor – as he is now known – will also leave his mansion in Windsor, Royal Lodge, as his links to convicted sex offender Jeffrey Epstein continue to cause controversy.

The statement concluded: “Their majesties wish to make clear that their thoughts and utmost sympathies have been and will remain with the victims and survivors of any and all forms of abuse.”

Asked whether this suggested King Charles believes Virginia over Andrew, her brother Sky Roberts said: “Absolutely, I think that he’s speaking very clearly in that statement when he says he’s with survivors out there.

“It’s an acknowledgment that something occurred, something has happened. There has been a shift,” he said.

Giuffre’s sister-in-law, Amanda Roberts, said: “To put that acknowledgment out for survivors is huge. We haven’t seen that from anyone, and to acknowledge that there are survivors in this situation is an acknowledgment that abuse did occur.

“It is the very first step for that justice for survivors. It is first the acknowledgment that something went on here. There was real trauma that happened to these young girls.”

In a posthumous memoir, Giuffre – who died earlier this year – repeated allegations that, as a teenager, she had sex with Mountbatten Windsor on three separate occasions. He has always denied any wrongdoing. He settled a civil case with Giuffre for a reported £12m with no admission of liability.

Amanda described the statement by the palace as a “victory” and “vindication for our sister”.

“We’re just so exceptionally proud of her, but then the sorrow hits because you wish she was here to share this moment together with her – a moment that she has been waiting for, for a very long time,” she added.

Women’s rights campaigners and advocacy groups also welcomed the move by the royal family, with some saying it sent an important message to survivors of abuse.

Gemma Sherrington, chief executive of Refuge, said it was “incredibly powerful to see survivors recognised so directly in a statement from the palace”, adding that it sent a message that “survivors matter, that their experiences are believed, and that they deserve to be at the heart of national conversations about abuse”.

Penny East, the chief executive at the Fawcett Society, said “it is a welcome acknowledgment that the real victims here are not embarrassed politicians or disgraced princes, but the women and girls who were sexually assaulted by entitled, misogynistic men.”

However, she added: “Removing a title, or moving house can never be viewed as true accountability or sufficient punishment. Indeed, one brave woman, Virginia Giuffre, has lost her life. It was a terrible tragedy, and a reminder of the profound impact sexual assault has on women and girls.”

Describing Giuffre’s character and fight for justice, Sky said she was a “strong warrior” who could also be cheeky and goofy.

“This is an ordinary girl from an ordinary family that did something extraordinary and I think this is something the world should be proud of.

“She was this strong warrior who refused to back down and refused to stay silent and we are finally getting that acknowledgment that she truly was a world hero.”

The palace declined to comment.

In the UK, Rape Crisis offers support for rape and sexual abuse on 0808 802 9999 in England and Wales, 0808 801 0302 in Scotland, or 0800 0246 991 in Northern Ireland. In the US, Rainn offers support on 800-656-4673. In Australia, support is available at 1800Respect (1800 737 732). Other international helplines can be found at ibiblio.org/rcip/internl.html