Robinson - of Laurel Drive, Craigavon in Co Armagh - also admitted acquiring criminal property, namely cash, on the same dates but was not asked to enter pleas to other charges.
Robinson, 25, from the British province of Northern Ireland, was addressing a London court hearing from prison a month after the 39 bodies were found in the truck on an industrial estate in Grays, about 20 miles (32 km) east of London.
The victims, 31 men and boys and eight women, were found on October 23 in an industrial park in Grays, Essex, not far from docks on the River Thames.
Maurice Robinson pleaded guilty at the Old Bailey to conspiring with others to assist illegal immigration between 1 May 2018 and 24 October 2019. The youngest victim was 15 years old and the oldest was 44.
The charge read as "an act or series of acts which facilitated the commission of a breach of immigration law by various persons".
Robinson also admitted acquiring criminal property between May past year and October 2019, but was not asked to enter pleas to other charges.
A second man from Northern Ireland, Christopher Kennedy, was also charged with their deaths yesterday.
Robinson was remanded into custody until a further hearing on 13 December.
"Kennedy, of Corkley Road in Darkley, County Armagh, Northern Ireland, is due to appear at Chelmsford Magistrates' Court on Monday 25 November".
The trailer had earlier arrived on a cargo ferry from the Belgian port of Zeebrugge.
Police in Vietnam have arrested 10 people there in connection with the deaths.
Robinson is also charged with conspiracy to commit human trafficking offences between 1 May, 2018, and 24 October, 2019.
He was charged with conspiracy to arrange people trafficking and conspiracy to break United Kingdom immigration law.
Officers also wish to speak to Ronan Hughes, 40, and his brother Christopher, 34, who are both on the run, and are wanted on suspicion of manslaughter and human trafficking in relation to the deaths.