Relatives of Hannah Witheridge, 23, and David Miller, 24, arrived in Bangkok today.
Police have advised them against viewing the bodies because damage from the murder weapon, a hoe, has made the young tourists' faces unrecognisable.
Former suspect and fellow Briton Christopher Alan Ware could be on a flight back home as early as tonight, with Thai Tourist Police helping to organise the flight plans for he and his brother.
Most interest now centres on a man of Asian appearance who ran back and forth several times down a road near the beach where the bodies were found early on Monday. Grainy black and white footage of the man is the only clue investigators now have.
Region 8 Police Commander General Panya Mamen said today: ''More detectives will be added to the team. We aim to interview everyone who was within 500 metres of the scene where the killing took place.''
The thought of a killer on the loose will perturb police and tourism authorities and trouble visitors planning on going to that part of Thailand.
Many unexplained aspects have yet to be threaded together.
Thailand's Deputy Commander of Police, General Jarumporn Suramanee, has raised the prospect that there could be more than one killer and more than one murder weapon.
With an autopsy confirming that Miller's body had water in the lungs, investigators believe he struggled with his killer in the sea. Yet if Ms Witheridge was alive at the time, she would have screamed and probably ran.
One report allegedly directly from the laboratory where the autopsies were carried out speculates today that two men had sex with Hannah Witheridge on the night she died and that the DNA on one matched the DNA found on a cigarette discarded nearby.
To end confusion, what investigators should consider is a daily media briefing for Thai and international journalists to clarify discrepancies and update on the latest information, much as the Malaysian authorities did after the disappearance six months ago of Flight MH370, until the killer or killers are caught.