Senior MPs have raised concerns that potentially hundreds of thousands of EU citizens could "fall through the cracks" of the Government's new immigration scheme.
Home Office ministers were warned that up to 200,000 EU nationals could be "left without status" if just 5% failed to register before the June 2021 cut-off.
Immigration Minister Caroline Nokes, when pressed to explain what would happen to those who failed to register in time, said there would be a "proportionate response".
The comment came as MPs heard details of the settlement scheme for EU migrants seeking to stay in the UK after the post-Brexit implementation period ends on December 31 2020.
Applicants will have to pay £65, which is the same as the current fee for a permanent residence document and £10.50 cheaper than the minimum for a standard British passport.
SNP home affairs spokeswoman Jo Cherry, speaking in the Commons, said: "There are potentially significant numbers of people who could fall through the cracks here. If just 5% of the estimated three million EU citizens living in the UK don't register by the deadline there would be a population of nearly 200,000 left without status."
Labour former minister Yvette Cooper, who chairs the Commons Home Affairs Committee, later raised the issue of children and asked what would happen in the event that a child was not registered.
She said: "Can she say whether this means that after that date they will not be lawfully resident here?
"Does she worry that this will mean they have lost legal rights and what action is she taking to prevent children who have grown up and lived here for many years losing their legal rights?"
Ms Nokes responded: "We will have absolutely have a proportionate response to those who have not registered before the end of June 2021 and we will be working extremely hard to make sure that as many are registered as possible."
Labour former minister Hilary Benn, who chairs the Commons Brexit Committee, asked ministers if the scheme would still stand in the event of a no-deal Brexit.
Ms Nokes said: "We are not anticipating failure, I think that is an important part of this.
"We have confidence that there will be a deal. We have reached an agreement with the EU guaranteeing the rights of EU citizens living in the UK and of UK nationals living in the EU and we do not expect that to be reopened."
Earlier in the question session, Ms Nokes explained that the Home Office would be "looking to grant, not reasons to refuse" applications.
She said: "Case workers will be able to exercise discretion in favour of the applicant where appropriate to minimise administrative burdens."
DETAILS OF POST-BREXIT SETTLEMENT SCHEME FOR EU NATIONALS REVEALED
The Government has published details of the settlement scheme for EU nationals and their family members seeking to stay in the UK after Brexit.
Here are the main steps in the application process:
The Home Office is designing an online application platform which it says will be simple and user-friendly. Applicants will be asked to provide their biographical information, declare whether they have any criminal records, and upload a facial photograph.
The process requires verification of the applicant's identity and nationality using a passport, ID card or other valid document. This can be done using a mobile app or through secure post.
Where possible, the applicant will be helped to demonstrate they have been continuously living in the UK using data held by HMRC and the Department for Work and Pensions. Where automated checks are not applicable or do not indicate the citizen has been continuously resident in the UK, documentary evidence will be required.
The Home Office will carry out checks against UK criminality and security databases in all cases. Applications will only be considered for refusal where someone has been convicted of a serious offence.
Officials hope to provide applicants with a response on whether their application has been successful within a fortnight. Evidence of settled status will be given to EU citizens in digital form - no physical document will be issued.
Where a valid application is refused, there will be the right to request an administrative review. Someone who has been refused status under the scheme can make a new application at any point before the end of June 2021. In addition, the Government is planning to introduce legislation so there will be a statutory right of appeal for applications made from March 30 next year.
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