Police detained a small group of suspected illegal immigrants in Market Harborough last Friday.
The four people - a man, a woman and two young children - were discovered hiding in a timber lorry at Glenmere Timber on Gores Lane in the town.
The lorry, originally from Lithuania, had crossed the Channel by ferry between Dunkirk and Dover, and was delivering timber from the continent.
The group, refugees from war-torn Kurdish Iraq, gave themselves up to Harborough police at around 10am on Friday, a police spokesman said.
The police then contacted the local Immigration Enforcement team, based at East Midlands Airport.
The woman and her two children, who are aged six and four, remain in the care of the Home Office while their cases are progressed.
The man, who the Mail understands was accompanying the other three but was not related to them, is being dealt with separately.
The Kurds, an ethnic group of around 30 million people, are spread throughout northern Iraq and Syria, western Iran and eastern Turkey. They are considered to be the largest stateless national group in the world.
The Kurds are fighting Islamic State to the south, and have had success in reversing the advance of Islamic State forces.
They are also fighting Turkish troops to the north-west and forces in Syria.