“She remembers what is was like to walk around London at night before she was married,” the palace added.
Tearful mourners have been gathering at the bandstand all day – with many placing flowers.
Ms Everard walked through Clapham Common on a way back from a friend’s house before disappearing on March 3.
A vigil at the bandstand was cancelled ahead of its 6pm start time on Saturday after the Met Police threatened to fine organisers £10,000 each.
Vigils had been organised across the UK in memory of the 33-year-old and to protest against violence against women.
Reclaim These Streets, who organised the Clapham vigil, said a “virtual gathering” would take place instead.
Meanwhile a fundraiser set up by the group for women’s charitable causes has already generated more than half its £320,000 target.
On Friday, a High Court judge refused to intervene on behalf of Reclaim These Streets in a legal challenge over the right to gather for a protest during coronavirus restrictions.
On Saturday, the group said that despite their attempts to work with police to ensure the Clapham vigil could proceed safely, they now felt it could not go ahead.
Ms Everard, who lived in Brixton, disappeared on March 3 after walking back from a friend’s home in Clapham.
Wayne Couzens, a serving Met Police officer, has been charged with her murder and kidnap.
The news sent shockwaves through the local community and many looked visibly shaken as they stood by the bandstand.
One woman tweeted: “We went to pay our respects and the whole of the bandstand at Clapham Common is woven through with flowers #saraheverard #reclaimthestreets”
Another Twitter user said: “People are threading their bouquets through the Clapham Common bandstand and already it is making the most beautiful monument to Sarah Everard and to all who knew and loved her.”
Couzens appeared at Westminster Magistrates’ Court on Saturday morning following his arrest on Tuesday.
Chief Magistrate Paul Goldspring remanded Couzens in custody to appear at the Old Bailey on March 16.
The Duchess’ appearance comes at a time of tumult for the Royal Family.
Her husband, the Duke of Cambridge, was forced to defend his family after the Duke and Duchess of Sussex gave an explosive interview to Oprah Winfrey.
During the interview Meghan Markle said a senior royal asked about her son’s skin tone before he was born.