The agreement came in a face-to-face discussion of the controversy surrounding the probe between David Cameron and military ruler General Prayuth Chan-ocha at a summit in Milan.
Detectives are expected to focus on independent checks of DNA samples central to the case against two Burmese men accused of the crime and their claims to have been mistreated.
Leeds University student David Miller, 24, and 23-year-old Hannah Witheridge were found dead on a beach of the holiday island of Koh Tao last month.
Court proceedings have reportedly started against the two suspects amid international concern about the way the case has been handled by the Thai authorities.
The Thai leader had previously rejected offers of help and insisted the UK no longer had “any more doubts” about the quality of the investigation following ambassador-level talks.
“They simply needed more time to understand it all because we managed to arrest suspects swiftly, even though it seemed impossible at the beginning,” he was reported to have said.
But diplomatic sources said he accepted the sending of a delegation of British police when pressed on the issue by Mr Cameron at the Asia Europe Meeting in Italy.
“Obviously it is for the Thai authorities to lead and carry out that judicial process,” a diplomatic source said.
“But it is important that it is fair and transparent and that both of the families can be reassured that it is the murderers that have been brought to justice.
“There are two areas we are particularly concerned about. One is the verification of the DNA samples of the suspects, making sure there is further independent verification.
“And the second is the investigation into allegations of mistreatment of the suspects.
“What the PM secured was agreement from the Thai PM that we can send some British police investigators to Kho Tao to work with the Royal Thai Police on this.”
The Burmese workers who have been charged with the killings were paraded in front of the cameras after apparently making confessions, which were reportedly later withdrawn.
The suspects, named in reports as 21-year-old bar workers Zaw Lin and Win Zaw Htun, were charged with three offences - conspiracy to murder, conspiracy to rape and robbery. But later reports - denied by the Thai police - suggested that a Burmese embassy official had formally retracted their confessions amid allegations the pair were tortured.