Some 15 of 68 migrants discovered inside lorries at Harwich International Port last week have already been deported, Immigration Minister James Brokenshire said.
Speaking in the House of Commons, Mr Brokenshire said some of the 68 migrants discovered at the port last Thursday were seeking asylum and investigations were ongoing into their claims.
The Conservative MP for Old Bexley and Sidcup added that two of the 68 were unaccompanied minors who are now in the care of social services.
Four lorry drivers arrested on suspicion of helping with illegal immigration have been released on police bail, pending further enquiries, Mr Brokenshire added.
The Polish lorry drivers arrested after 68 suspected illegal immigrants were found locked in their vehicles have been released on bail.
The four were taken in to custody after the 35 Afghan nationals, 22 Chinese nationals, 10 Vietnamese and one Russian passenger were discovered at Harwich International Port in Essex on Thursday evening.
However, after almost two days of being questioned by authorities, the drivers who were arrested on suspicion of facilitating illegal immigration were bailed until 2 July.
The incident was described as one of the "biggest single finds of clandestines coming into the UK" by Bernard Jenkin, MP for Harwich and North Essex.
The arrest of 68 migrants in four lorries at the Essex port of Harwich has highlighted the vulnerability of ports on England's east coast to illegal immigration.
Scores of big commercial lorries take the ferry route from Holland to England every week, making it a prime potential target for traffickers.
ITV News UK Editor Rohit Kachroo reports on the migrants' route to England's eastern seaboard.
A lengthy asylum process has begun to determine whether 53 adults and 15 children smuggled into the UK in lorries carrying Polish washing machines can remain in the country.
The suspected illegal immigrants from Afghanistan, China, Vietnam and Russia were found during a routine search at Harwich International Port in Essex last night.
They had been brought into Britain from Holland in four vehicles - a journey which the local MP claims sees 94% of lorries travel through the port unchecked.
ITV News Correspondent Juliet Bremner reports from Harwich.
Fifteen children and 53 adults - including two pregnant women - were found locked in four lorries in what an MP has descibed as one of the "biggest single finds of clandestines" trying to cross into the UK.
The suspected illegal immigrants were hidden in lorries carrying Polish washing machines during a routine search at Harwich International Port in Essex yesterday evening.
The MP for Harwich and North Essex, Bernard Jenkin, said the UK government would try to deport them all, but said it was like "every single one of them" would claim asylum, lengthening the process.
It was "one of the biggest single finds of clandestines coming into the UK in this fashion", he added - and warned that 94 per cent of trucks coming through the port go unchecked, meaning it was possible many migrants had managed to enter the country that way.
Four Polish lorry drivers have been arrested on suspicion of helping with illegal immigration.
Officers from the British Red Cross are supporting the 68 people found inside lorries at Harwich International Port, as Border Force officials continue their investigations.
The charity's volunteers have given the 53 adults and 15 children provisions including blankets, food and hygiene packs, as well as providing emotional support.
The suspected illegal immigrants were found locked inside four separate lorries during routine checks yesterday evening.
The discovery of 68 suspected illegal immigrants inside lorries at Harwich International Port follows the deaths of two illegal immigrants at the same port in February last year.
Artur Doda, 24, and Leonard Isufaj, 27, both from Tirana, Albania, were seen leaping from one of the world's largest ferries, the Stena Britannica, about 500 metres off Harwich.
They had been found in the back of a lorry along with 13 others of mixed nationalities as it entered the port six hours earlier.
In August last year, 35 immigrants, whose ages ranged from one to 72, were discovered in a container at Tilbury Docks in Essex.
One of them, 40-year-old Meet Singh Kapoor, from Afghanistan, was found dead.
Later the same month, one person was taken to hospital after 13 people were found in the back of a lorry at the Dartford Crossing in Kent.
Ferry firm Stena Line has confirmed that 68 suspected illegal immigrants discovered at Harwich International Port were found inside lorries travelling on one of its ships.
A Stena Line spokeswoman described the Stena Hollandica as a "supership" that carries both passengers and freight.
Following earlier reports from East of England Ambulance Service that the 68 were found inside one container, the Home Office confirmed that they were discovered "during a proactive search of four lorries".
Fifteen children and two pregnant women were among the 68 suspected illegal immigrants discovered by Border officials at Harwich International Port.
The suspected stowaways - 35 Afghan nationals, 22 Chinese nationals, 10 people from Vietnam and one Russian - were found during a "proactive" search of four lorries, a Home Office spokesperson said.
Four Polish nationals who were driving the vehicles were arrested on suspicion of facilitating illegal immigration.
They are being questioned by the Home Office’s criminal investigations team at separate police stations.
Four Polish lorry drivers have been arrested on suspicion of immigration offences after Border Force officers found 53 adults and 15 children during a search of lorries which had arrived at Harwich port from Holland, the Home Office said.