Tony Witheridge wept as images of his daughter’s body were shown on the third day of the trial of two Burmese migrants.
Zaw Lin and Wai Phyo, both 22, deny murdering Miss Witheridge, 23, from Norfolk, and David Miller, 24, from Jersey.
Both have retracted their initial confessions, saying they were extracted through beatings and threats, which police deny.
Mr Miller and Ms Witheridge’s bodies were found on a beach on the island of Koh Tao last September. A forensic police officer told the trial of the severe injuries Miss Witheridge suffered and of evidence she had been raped.
Mr Miller’s body was discovered with severe head injuries several metres away, he said.
Speaking at the court, Mr Miller’s father Ian said he and his wife Sue had come “with an open mind”, adding that it had been an emotional time for the family.
“There has been lots of chit-chat on the internet. We are here for David because of his tragic death.
“We’ll go with the flow as much as we can. We won’t comment on the trial process. We’ll be dignified for David.”
Mrs Miller said: “It’s been hard, very hard. Part of the reason for coming out was to go to Koh Tao. We had one day on Koh Tao; it was really hard.”
The court is expected to hear what happened to vital DNA evidence that links the two Burmese defendants to Miss Witheridge’s body.
Authorities have stated that they are possession of the evidence, disputing reports that it might have been lost.
The court was expected to rule yesterday on a defence request to re-examine the DNA.
“It is not lost,” national police chief General Somyot Poompanmoung told reporters in Bangkok. “I repeat: nothing is lost.”
Gen Somyot called it a misunderstanding that stemmed from foreign media covering the case who might have poor Thai language skills.
He said the local police investigator, Lieutenant Colonel Somsak Nurod, was vague in his testimony and therefore was misinterpreted.
Lt Col Somsak was no longer in possession of the DNA evidence because he sent it to the Forensics Medicine Institute in Bangkok, Gen Somyot said.
“Nothing is missing. It’s a misunderstanding,” the police chief said.
Under intense pressure to catch the murderers, Thai police carried out DNA tests on more than 200 people on Koh Tao before arresting the two Myanmar migrants in early October.
From the start, investigators faced a variety of criticism, including failing to secure the crime scene and releasing names and pictures of suspects who turned out to be innocent.
Prosecutors say the DNA evidence, collected from cigarette butts, a condom and the bodies of the victims, links the men to the killings, and defence lawyers have been asking to re-examine that evidence since April.
Briton Andy Hall, a migrant rights activist working with the defence, said that handing over the DNA evidence was crucial.
“Without the samples, it undermines the opportunity of the defence to get a fair trial,” Mr Hall said. “More importantly, if it is not provided, or if the forensics material is used up, it would undermine the credibility of the whole investigation.”