Ronan Hughes, 40, and his brother Christopher, 34, from Armagh are wanted on suspicion of manslaughter and human trafficking, Essex Police said.
"Finding and speaking to the Hughes brothers is crucial to our investigation," said Detective Chief Superintendent Stuart Hooper.
"At this time we believe they are in Northern Ireland but they also have links to the Irish Republic. If you know where they are or have any information about their whereabouts I need you to call my team."
On Monday, the truck's driver Maurice Robinson appeared in court accused of manslaughter and money laundering as well as accusations of conspiracy to traffic people and conspiracy to assist unlawful immigration.
For the latter alleged offenses, the charge sheet stated that he had conspired with Ronan Hughes and others, prosecutors said.Detectives investigating the deaths have arrested three other people apart from Robinson but they have since been released on police bail. Irish police have also arrested a man in connection with the investigation.