Three million EU citizens living in the UK will need to have some form of documentation following Brexit, the Home Secretary Amber Rudd has admitted.
The process could cost the taxpayer £100 million a year and require another 3,000 Home Office staff, the Liberal Democrats said.
The "formidable task" could amount to the equivalent of 140 years of work at recent rates of processing, according to estimates by the Migration Observatory at the University of Oxford.
Responding to a question from Brexit select committee chairman Hilary Benn in the Commons, Ms Rudd said: "There will be a need to have some sort of documentation... but we are not going to set it out yet.
"We are going to do it in a phased approach, to ensure that we use all the technology advantages that we are increasingly able to harness, to ensure that all immigration is carefully handled."
Meanwhile Ms Rudd said foreign students are likely to remain in the government's target to cut immigration to the tens of thousands amid growing clamour for them to be separated.
Over the weekend, Foreign Secretary Boris Johnson backed excluding them from the overall numbers - a stance also taken by Chancellor Philip Hammond.
Ms Rudd said: "Students play an important role in contributing to the economy and are most welcome in the UK.
"The internationally-recognised definition of a migrant is someone coming here for over 12 months, so they are likely to stay within that definition, although I'm aware there are different views on this matter."