British police who travelled to Thailand to review the probe into the murders of Hannah Witheridge, from Great Yarmouth, and David Miller are due to return to the UK, having completed their work "as far as possible".
Officers from the Metropolitan Police flew out last month to work with the Royal Thai Police after an agreement between David Cameron and military ruler General Prayuth Chan-ocha.
It followed international concern about the way the case has been handled by the Thai authorities.
Mr Miller, 24, from Jersey, and 23-year-old Ms Witheridge, from Great Yarmouth in Norfolk, were found dead on a beach on the holiday island of Koh Tao in September.
Two Burmese men, named as 21-year-old bar workers Zaw Lin and Win Zaw Htun, were charged with the killings and paraded in front of cameras after apparently making confessions, but these were later reportedly withdrawn.
UK police concerns are understood to have been around the verification of DNA samples of the suspects and allegations of their mistreatment.
Scotland Yard said officers will compile a report from their review.
Thai police are offering a reward of more than £13,000 to try and catch the killers of two British tourists found dead on the island of Koh Tao.
The bodies of 23-year-old Hannah Witheridge, from Hemsby in Norfolk, and David Miller, from Jersey, were discovered on a beach on September 15.
A bloodstained garden hoe, believed to be the murder weapon, was found nearby.
A group of Thai footballers are the latest people to be questioned in connection with the investigation.
Police colonel Kissana Phathanacharoen said a reward of 700,000 baht, roughly £13,300, is now being offered for information which leads to the arrests of the culprits.