The lorry travelled from Bulgaria, arriving in the UK via Holyhead on Saturday.
The lorry driver, a 25-year-old man from Northern Ireland, has been taken into custody on suspicion of murder.
Early indications are that 38 adults and one teenager have died.
Ch Supt Andrew Mariner said officers were trying to identify victims but anticipated a ‘lengthy process’.
Waterglade Industrial Park has been cordoned off as a result of this incident.