The murder of two young British tourists on a Thai island will make many travellers think twice before travelling to the South East Asian nation on holiday, Thai police say.

The bodies of Hannah Witheridge, 23, and David Miller, 24, were found last week with severe head wounds near where they were staying on the southern island of Koh Tao, known for its coral reefs and diving.

"People coming to Thailand will think twice about travelling here after a murder," lieutenant colonel Kissana Phatanacharoen, deputy spokesman for the Royal Thai Police, said.

"Given the enormous media interest in this case that is only natural."

The killings are the latest blow to Thailand's vital tourism industry, denting the country's image as the happy-go-lucky paradise often referred to as the "land of smiles".

Tourism had already been battered by political street protests and military rule that have kept travellers away from the capital Bangkok and seen hotel occupancy rates plummet.

Prime minister General Prayuth Chan-ocha, whose coup in May toppled the remnants of a democratic government, warned tourists last week Thailand was not as safe as they imagined.

He also apologised for criticising tourists who wear bikinis, comments that sparked an international outcry.

Thai authorities have made no arrests and reported little progress in solving the crime.

DNA samples related to the case had been sent to Singapore, where testing is quicker, Mr Kissana said. Interpol Thailand had joined the investigation, he added.

"We're reconstructing the steps of both victims, their activities on the island, who they met, who they flirted with, who they learned to dive with," said Mr Kissana.

The number of tourists arriving in Thailand in August fell 11.9 per cent from a year earlier after a 10.9 per cent drop in July, according to the Department of Tourism.

Reuters