In a statement, Ms Powers said: “University College staff and students are extremely saddened by the tragic death of Rosie Roche.
“Rosie was a first year student studying for an English Literature degree. Rosie had settled into the University and College beautifully and had lots of friends.
“She was loved for her creativity, energy, her love of books, poetry and travel among many other talents. She will be sorely missed.
“Our thoughts and condolences are with Rosie’s family and friends, and we are offering support to those affected at this extremely difficult time.”
Rosie was the granddaughter of Diana, Princess of Wales’s uncle, making her a second cousin of the Prince of Wales and Duke of Sussex.
Her family said in a death notice that she was the “darling daughter” of Hugh and Pippa and an “incredible sister” to Archie and Agatha.
A Wiltshire Police spokesperson said: “There are no suspicious circumstances, and our thoughts are with her family. We would ask that their privacy is respected at this terrible time.”