Hundreds of thousands of European migrants who are eligible to stay in the UK after Brexit may struggle to provide official documentation to support their application, Oxford academics have warned.

The Migration Observatory, based at the university, claimed EU nationals will face difficulties showing they have been living in Britain before departure from the bloc in March 2019.

For example, people without bank accounts or leases may have only informal proof of address such as letters from friends.

The research group’s director Madeleine Sumption said: “Most EU citizens should have little trouble getting their status resolved if the simplified system the Government has proposed goes ahead.

“But there are still big questions about what will happen to the minority who don’t have official evidence that they have been living in the UK.

“It’s impossible to estimate exactly how many this will be. But even if it is only a few per cent of the total, the numbers of applicants affected would run into the tens or even the hundreds of thousands.”

She said the registration process for EU citizens “will be prone to controversy”, adding: “Any indication of fraud would be quick to hit the headlines, but if the burden of proof is high and eligible people lose their legal status, this will also undermine trust in the system.”

EU citizens who arrive by March 29 2019 and have been continuously and lawfully living in the UK for five years will be able to apply to stay indefinitely by getting “settled status”.

Those who have been in the country for less than five years before the exit date will be able to apply to remain until they have reached the five-year threshold.

Officials are working to establish a new system from scratch to process potentially more than three million applications from EU citizens and their families.

The agreement struck by the UK and the EU last week makes clear that the arrangements will be “transparent, smooth and streamlined”.