A Givealittle page has been launched to try to raise money to fly Mr Annesley and his daughter, 5-year-old Piper-Jean, to the UK to attend the funeral.
Mr Annesley said he was overwhelmed by the generosity of those who were donating to enable him and Piper-Jean to attend the funeral.
Mr Annesley said he had initially been opposed to the idea of people giving him money, but once the page was set up, he was grateful.
His sister was bubbly, intelligent, and interested in politics, he said.
"She was one of those people everybody liked, one of those people that never speaks bad about people."
They had kept in touch, despite spending most of their lives in different countries.
"All my life I have travelled over there [to England], I don't know how many times."
He did not know when the funeral would be held, but it was likely to be at least three weeks from now, he said.
The Givealittle page has raised $7535 in the five days since it was created.
The London Evening Standard reported that Thai officials said a preliminary post-mortem had not shown signs of "foul play" or sexual assault.
Ms Annesley's mother Maggie said Christina was two weeks into a solo gap year trip to Southeast Asia and Australia.
"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 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.
The description on the fundraising website said Aaron Annesley had flown to the UK for his brother's funeral a few years ago.
- Additional reporting Otago Daily Times
