The 20-year-old cousin of Prince William and Harry was found dead at her family's Norton, Wiltshire home with a firearm recovered near her, media reports said.

Rosie Roche is the granddaughter of Princess Diana's uncle.

Her body was recovered on July 14.

She was found by her mum and sister after she had been packing to go away with friends, reported The Sun.

An inquest was opened at Wiltshire and Swindon coroner’s court and adjourned until October 25, the British newspaper reported.

The 20-year-old was studying English Literature at Durha University.

Area coroner Grant Davies told The Sun police “have deemed the death as non-suspicious and there was no third-party involvement”.

Professor Wendy Powers, Principal of Durham's University College said the students and staff members felt saddened by her demise.

“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," the Principal was quoted as saying by The Sun.

“She was loved for her creativity, energy, her love of books, poetry and travel among many other talents. She will be sorely missed," the principal said.