The families of the two Myanmar men charged with the murder of two British tourists have ordered an investigation into claims they were tortured by Thai police, according to the suspects' lawyer.

British tourists David Miller, 24, and Hannah Witheridge, 23, were both found dead on a beach with horrific head injuries after attending a party on the resort of Koh Tao in September.

Burmese migrants Win Zaw Htun and Zaw Lin have been accused of killing the pair and have been detained by authorities who say they confessed to the murders. But the men claim they were forced into confessing their part in the deaths after being brutally tortured.

"When they visited their sons they were told that they did not commit the crime. They were tortured by police and the police interpreter," the lawyer for both suspects, Surapong Kongchantuk, said.

"I would like the Department of Special Investigation to take up the case," he added.

Thai police deny that the suspects were tortured during their interrogations and have stated that the pair are being treated well in prison.

As a result of the pair's murder, all beach parties are to be banned except the Full Moon Party on Phangan Island because of the detrimental effect on the country's tourism industry, according to Chatpong Chatputhi, the governor of Surat Thani Province.

"We've reached a point where we need to clean up the image of tourism in the province including beach parties that can get out of control and lead to violence," he told Reuters.

"This is aimed at tourists' safety. Sometimes these parties are held at secluded locations that are difficult to reach and where we cannot offer adequate protection."

Tourism represents 10% of Thailand's gross domestic product (GDP) and the ban comes at a time when martial law is still in place following a coup by the military junta in May.