The London Evening Standard reported that Thai officials said a preliminary post-mortem had not shown signs of "foul play" or sexual assault following a three-hour examination in Bangkok.
Ms Annesley's mother Maggie said Christina was two weeks into a solo gap year trip to South East Asia and Australia due to last four months.
She told the London Evening Standard that her daughter was intelligent.
"She had straight As in school and loved to party. She was so kind, so witty with a dry sense of humour.
"The trip was supposed to last four months and she was going to visit some of my friends in Australia - her father is from New Zealand and she held a dual passport.
"She loved writing and was so talented. She was thinking of becoming a journalist, which she would've been brilliant at."
The New Zealand death notice for Ms Annesley said the family were "astounded by the interest in our lovely daughter by the UK press and all the messages of her achievements".
"A loving and bright light has been taken from us."
No funeral had been organised as Ms Annesley's body remained in Thailand.
The Ministry of Foreign Affairs and Trade said it was aware of the death of a dual United Kingdom and New Zealand citizen in Koh Tao and consular support was being provided by the British Embassy.
A Givealittle page has been launched to try to raise money to fly Ms Annesley's brother Aaron and his daughter Piper-Jean to the UK to attend the funeral.
The page was created five days ago by his sister-in-law Jacki Ryan in Wellington and has so far raised $7,535.
The description on the fundraising website said Aaron has flown to the UK for his brother's funeral a few years ago.
"We would like to help him and his young daughter Piper-Jean to travel back to the UK to be with family at this terrible time to support each other."
Koh Tao is the same island where British backpackers Hannah Witheridge, 23, and David Miller, 24, were killed in September, sparking an investigation by local police who were criticised for failing to properly secure the crime scene.