The 39 people found dead in a refrigerated trailer in Essex were Chinese nationals.
Police are continuing to question lorry driver Mo Robinson, 25, on suspicion of murdering the eight women and 31 men.
Officers in Northern Ireland have raided three properties and the National Crime Agency said it was working to identify “organised crime groups who may have played a part”.
The trailer arrived in Purfleet on the River Thames from Zeebrugge in Belgium.
Ambulance staff discovered the bodies in the container at Waterglade Industrial Park in Grays on Wednesday.
Police said the tractor unit – the front part of the lorry – entered the country via Holyhead in Wales on Sunday, having travelled from Dublin.
The lorry has been moved to a secure site at Tilbury Docks so investigations could be “conducted in peace” and to give the “utmost dignity to those within the trailer”.
Essex Police said it was the largest murder investigation in the force’s history and the victims were all “believed to be Chinese nationals”.
It said formal identification of the 39 people, one of whom is a young adult woman, “could be a lengthy process”.
China’s ambassador to the UK Liu Xiaoming tweeted that the embassy had read the reports of the deaths “with heavy hearts” and was in close contact with British police.
Police officers and councillors have signed a book of condolences which was opened at Thurrock Council’s chambers.
A vigil is also being held at 18:00 outside the Home Office to “call for urgent action to ensure safe passage” for people fleeing war and poverty.