Registering more than three million EU migrants already living in Britain would present the Government with a huge administrative task, according to a new report.
Experts looked at the existing regime for applying for permanent residence to examine possible issues that could arise if any new system was rolled out following the Brexit vote.
Their analysis suggests that if all the European Economic Area (EEA) citizens living in the UK at the beginning of 2016 applied for permanent residence in the same year, this would amount to the equivalent of around 140 years of work at recent rates of processing.
Britain is expected to seek to introduce controls on free movement rules following the outcome of the referendum in June, but details of the system have yet to be outlined.
Madeleine Sumption, director of the Migration Observatory at the University of Oxford, said: "Depending on how long Brexit negotiations take, the Government may need to register EU citizens already living here quite quickly.
"Given the sheer number of EU citizens who would need to register and the potential complexity of the process, this will be a formidable task."
The Observatory looked at the existing regime through which EU nationals apply for permanent residence. Under the rules those who have lived continuously in the UK for at least five years automatically have a permanent right to reside.
The paper said that while the actual process in coming years may be "quite different", examining the current process "gives an insight into the kind of issues that could arise as any future registration mechanism is implemented".
Assuming free movement comes to an end after the exit process is formalised, EU citizens may need to obtain documents demonstrating their residence rights within a relatively short period of time in order to distinguish themselves from newly arriving EU citizens who do not continue to enjoy free movement rights, according to the study.
It said that over the past five years the Home Office has been processing an average of 25,500 permanent residence applications per year from EEA citizens and their family members.
The Observatory said its analysis showed the total population of citizens of EEA countries, plus Switzerland, living in the UK was more than 3.5 million by the beginning of this year.
If all of those were to apply in the same year this would be "equivalent to approximately 140 years' worth of permanent residence applications", the report said.
It added: "While, of course, a large and dedicated team would be expected to take this process on to deal with applications much more rapidly, these figures illustrate the scale of the administrative challenge ahead."
The commentary said that while the process could be similar to the current permanent residence application, it is also possible that a different or simpler procedure will be introduced.
Meanwhile, the report suggested that if existing rules for registering EU citizens as permanent residents are used as the model for a post-Brexit process, some groups may not qualify despite having lived in the country for several years.
It said: "While most cases involving people employed in the UK in stable, full-time jobs have the potential to be relatively straightforward, many EU citizens may find themselves in more complex situations. This includes students, self-sufficient people, low earners and the self-employed."
A Home Office spokeswoman said: "We have been clear that we want to protect the status of EU nationals already living here, and the only circumstances in which that wouldn't be possible is if British citizens' rights in European member states were not protected in return.
"We are about to begin these negotiations and it would be wrong to set out further unilateral positions in advance. But there is clearly no mandate for accepting the free movement of people as it has existed up until now."