Clemmie Hambro, 44, said she was "completely horrified" by the revelations against Epstein.
It comes after it emerged that she took two flights on Epstein's jet in 1999, according to flight logs seen by the Daily Mail that were released in court proceedings.
The records apparently show that she visited the convicted sex offender's New Mexico ranch and Little St James in the US Virgin Islands, where he is said to have spent years abusing young girls.
Ms Hambro, Sir Winston Churchill's great-granddaughter, told the publication in a statement that her "heart breaks for all the survivors".
She said that she did not suffer or witness any abuse, adding that she hopes those who did "get the justice they so deserve".
At the point she made the trips in 1999, Ms Hambro was a 23-year-old employee at Christie’s auction house in New York.
She said she visited the ranch on a "work trip" to help Epstein decide what art he wanted to buy while another was a "personal invitation" to the Caribbean island.
Eight years before his conviction, records show Epstein was with Ms Hambro on both flights and that British socialite Ghislaine Maxwell, 58, was also present for one trip.
The flight logs unearthed by the Mail reveal that on February 21, 1999, Ms Hambro flew with Epstein, Maxwell and two other women from Santa Fe, where Epstein had his ‘Zorro Ranch’, to New York’s Teterboro airport.
A month later, on March 21, she was on his jet from St Thomas, used by Epstein to access Little St James, to Teterboro.
In a statement last night, Ms Hambro told the publication: "My heart breaks for all the survivors, now I know what happened on that island.
"In the course of those two trips, I was not abused, nor did I see anyone abused, or anything untoward happen, with minors or otherwise.
"I have been completely horrified about the revelations of his conduct since then. I was clearly very lucky, my heart goes out to those who were abused by him, and I trust they get the justice they so deserve."
Ms Hambro was the youngest bridesmaid at the wedding of Lady Diana Spencer and Prince Charles in July 1981 aged 5.
Little St James is at the centre of abuse allegations against Epstein, who took his own life in jail a year ago.
Maxwell is awaiting trial for aiding Epstein in his abuse. She denies all the allegations.