More than 2.7m Europeans have applied for permanent residence in the UK under the EU Settlement Scheme as the country prepares to leave Europe.
Some 163,300 EU citizens applied last month to live and work in the UK after Brexit.
Of the applications dealt with in December, 55% were granted permanent leave to remain in the country, called settled status, and 44% were granted pre-settled status - which means they have temporary leave to remain and would need to apply again for permanent permission at a later date.
The government faces a big challenge getting all EU citizens through the Settlement Scheme"
Around a third of EU nationals living in the UK have yet to secure settled status to remain in the country. According to research compiled by the AIRE Centre, a legal charity specialising in European Law, the failure to secure their status before next year's deadline is a major threat to the stability to UK companies.
EU nationals make up 7% of the UK labour market, with several key sectors of the economy reliant on European workers. The UK retail and manufacturing industries are among the most exposed to the problem with 26% and 24% of workers respectively coming from Europe, while 21 per cent of construction industry workers come from the EU, the report quoted by iNews said.
There is currently no salary threshold to apply for settled status in the UK. However, if the EUSS deadline is missed by lower-paid EU workers, it is predicted they may not be permitted to settle in the UK ever again, "which could be catastrophic for business and these individuals", experts warned.
Six applications have now been refused on "suitability grounds", the Home Office report said.
Matthew Evans, director at The AIRE Centre, said: "The future salary threshold for EU nationals coming to work in post-Brexit Britain has been well publicised at a possible £30,000. For many, their income will fall below this level and understandably, they are worried about completing their applications for fear of being rejected.
"It is vital we debunk this myth, and employers take action to ensure their workers are guided through the EUSS process to secure the status and rights that they are eligible for and to prevent disruption to business operations."
Madeleine Sumption, director at the Migration Observatory, University of Oxford, added: "The government faces a big challenge getting all EU citizens through the Settlement Scheme. Regardless of how easy it is to apply and how well the scheme is communicated, there will inevitably be people who simply don't realise that they have to do it.
"This challenge is compounded by the fact that there are no accurate figures on how many people are eligible to apply: the most commonly used estimate of 3.4 million is almost certainly too low. So it's possible that hundreds of thousands of EU citizens could fail to apply without this being clear from the data.
"One of the big questions for the next couple of years will therefore be whether the deadline is extended or, as some have suggested, removed entirely."
The warning comes after the European parliament raised concerns that EU nationals living in the UK could face discrimination in jobs and housing post-Brexit due to the Government's refusal to issue physical documentation proving their rights.