BANGKOK (REUTERS) - Thailand has agreed to allow British police to join an investigation into the murder of two backpackers on a Thai island, after local authorities came under criticism for their handling of the case.

British police experts will travel to the holiday island of Koh Tao to help investigate the murder of Britons Hannah Witheridge, 23, and David Miller, 24, on a beach in September, according to a statement from the office of British Prime Minister David Cameron.

The agreement was reached after a Cameron raised the issue with Thai Prime Minister Prayuth Chan-ocha at an international summit in Milan this week, the statement said.

It did not provide further details on how many officials would travel to Thailand or what kind of assistance they would provide.

Details of the agreement were yet to be worked out, but would involve "close coordination" between Thai authorities and the British Embassy in Bangkok, said Col. Weerachon Sukondhapatipak, the deputy spokesman of Thailand's Army, which seized power in a May coup.

Thai authorities have been criticised for what has been seen as a shambolic investigation into the murders, including a slew of false leads and concerns over lapses in investigative procedure.

Police now allege that two workers from neighbouring Myanmar, Zaw Lin and Win Zaw Htun, both 21, committed the murders.

Police have said they have obtained confessions as well as DNA evidence from Witheridge that matches both men, although concerns have been raised over the validity of the evidence.

The men have been charged with murder, rape and robbery.