The 34 people found alive in a shipping container at Tilbury docks are in the care of the Home Office after being interviewed by police and are in the process of applying for asylum in the UK.
"We are continuing to provide expert support, along with the National Crime Agency, to the Essex Police investigation into the discovery," a Home Office spokesperson said.
"This tragic incident is a reminder of the devastating human consequences of illegal migration and we will do all we can to help bring those responsible to justice," they added.
The Home Office does not comment on individual cases and any decision made will not be announced publicly.
Home Secretary Theresa May said the government would look carefully at an Arbitration Tribunal's decision to award a £224 million pay out to US defence firm Raytheon.
In a letter to the MP Keith Vaz, she said: "The Government stands by the decision to end the eBorders contract with Raytheon. This decision was, and remains, the most appropriate action to address the well-documented issues with the delivery and management of the programme."
She added: "We are looking carefully at the tribunal's detailed conclusions to see if there are any grounds for challenging the award."
The Home Secretary said key milestones had been missed by Raytheon in 2010 and parts of the programme were running at least a year late.
"The situation the Government inherited was, therefore, a mess with no attractive options," she said. "All other alternatives available to the Government would have led to greater costs than the result of this tribunal ruling."
The Home Office is to pay out £224 million to defence firm Raytheon, including nearly £50 million in damages, after an Arbitration Tribunal found the Government department unlawfully terminated the company's contract to provide the eBorders programme.
A senior Home Office civil servant faces a grilling by MPs over its handling of child abuse allegations made over a 20-year period.
Permanent secretary Mark Sedwill will appear before the Home Affairs Select Committee to face questions over the quality of a review he commissioned last year.
As Theresa May announced new inquiries to Parliament yesterday, the Home Secretary said she was confident that the work commissioned by Mr Sedwill was "carried out in good faith".
However, she added that with "allegations as serious as these the public need to have complete confidence in the integrity of the investigation's findings".
The Home Office has hit back at claims changes it introduced to law which check and prevent sexual offenders from working with children have allowed predators to slip through the net.
It remains the case that anyone committing the most serious offences is still automatically barred from working closely and unsupervised with children.
The coalition Government introduced changes to the barring regime to apply common sense levels, but if someone applies to work with children any serious criminal records or police information are still considered when checks are carried out and, if necessary, they will be barred.
The changes strike an appropriate balance between avoiding unnecessary intrusion into people's lives and ensuring that children and vulnerable groups are protected.
A Nigerian mother who appealed against her removal from the UK, saying she feared her daughters would be subjected to female genital mutilation, has been deported.
The Home Office released a statement saying that Afusat Saliu "was not considered to be in need of protection".
The statement also pointed out that Ms Saliu's appication to stop deportation had been turned down by the courts on several occasions.
"The case has gone through the proper legal process and our decision has been supported by the UK courts on five separate occasions, while the European Court of Human Rights declined an application to halt the removal.”
"We can now confirm that a Nigerian family were successfully removed to their country of origin today."
Supporters of Afusat Saliu, the mother of two who fears her daughters will be subjected to female genital mutilation in her homeland of Nigeria, believe she was deported last night, the Guardian has reported.
A Home Office spokesperson said:
We consider every claim for asylum on its individual merits and in this case the claimant was not considered to be in need of protection.
The case has gone through the proper legal process and our decision has been supported by the UK courts on five separate occasions, while the European Court of Human Rights declined an application to halt the removal.
Anj Handa, a friend of Afusat Saliu, who set up the petition on campaigning website Change.org, said:
We have been thwarted at every turn and the Government has failed on so many counts in this case.
The Home Office has failed to stick to its own guidelines on so many counts and have failed Afusat and her daughters miserably.
The Government had a chance to show leadership on the issue of FGM and again have failed miserably.
A mother who fears her two daughters will be subjected to female genital mutilation in her native Nigeria has been told she will be deported tonight.
Afusat Saliu, 31, and her two daughters Bassy, four, and Rashidat, two, were seized by officials on Wednesday and were due to be flown to Lagos but were given an overnight reprieve.
Human rights activists representing Ms Saliu said that she was expected to be deported with her daughters at 7pm from Heathrow airport.