The 39 people found dead in a refrigerated trailer in Essex were Chinese nationals.
Police have been granted an extra 24 hours to question lorry driver Mo Robinson, 25, on suspicion of murdering the eight women and 31 men.
Three properties in Northern Ireland have been raided and the National Crime Agency is working to establish if "organised crime groups" were involved.
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 just after 01:30 BST 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.
Speaking after a magistrate granted Essex Police more time to question Mr Robinson on Thursday, Deputy Chief Constable Pippa Mills said her priority was "preserving the dignity of the 39 people who have died and ensuring that we get answers for their loved ones".
Councillor Paul Berry said the village of Laurelvale in County Armagh, where the Robinson family live, was in "complete shock".
He said he had been in contact with Mr Robinson's father, who had learned of his son's arrest on Wednesday through social media.
"The local community is hoping that he [Mo Robinson] has been caught up innocently in this matter but that's in the hands of Essex Police, and we will leave it in their professional hands to try to catch the perpetrators of this," he said.
The lorry has been moved to a secure site at Tilbury Docks and police are due to begin the process of moving the bodies to a mortuary at Broomfield Hospital in Chelmsford.
They will be taken by private ambulance so that post-mortem examinations can take place, with the force expecting all the bodies to have been moved by the weekend.
The firm said it had given Essex Police the details of the person and company they had leased it to.