Detectives investigating the deaths of at least 20 Chinese cockle pickers in Lancashire say their families cannot come to terms with how they died.
It is hoped the victims of the tragedy will be identified using DNA
Bereaved relatives told Lancashire officers who visited them in China that they believed they had fishing permits and were being looked after.
Detective Chief Inspector Steve Brunskill confirmed that up to 23 cocklers may have died in rising tides.
He said DNA tests should allow formal identification by the end of May.
The bodies of 20 cocklers have so far been recovered from the sands at Morecambe Bay.
Inquest to open
Tests are being carried out on a further body found on 3 May.
Police say initial studies show the body found at the weekend was probably the 21st victim of the tragedy.
Once DNA analysis on all the victims is complete, Mr Brunskill said he would compile a report for the coroner who was likely to open an inquest in early June.
He revealed the families had spoken of their desire to have the bodies of their loved ones returned to them.
But the high cost of flying the bodies home once the criminal investigation is complete posed an obstacle to many, he said.
Mr Brunskill, who led a party of eight officers to China to gather the DNA samples, said co-operation with the Chinese government and police had been "excellent".
But he said the families were unable to comprehend how the tragedy happened.
He said: "They could not understand how this could happen in this country.
"As far as they were aware, fishing permits had been issued and they were entitled to be out there working and someone must be responsible for them."
Some of the cocklers had been here illegally, while others were legal, said Mr Brunskill, but gave no further details.
But he revealed that Chinese police believed it more likely that so-called Snakehead gangs outside China had been responsible for organising the entry of some into Britain.
The cocklers died when they were caught in fast incoming tides at night, off Hest Bank on the bay, early in February.
Councillors in Lancaster have met this week to discuss measures to avoid a repeat of the tragedy.