Tens of thousands of EU nationals have been granted permission to continue living in Bedford ahead of this month's application deadline, figures show.
But a research hub at York University warns that many people across the UK will miss the fast-approaching post-Brexit "cliff-edge" and risk becoming illegal migrants overnight.
Around 20,860 people successfully applied to the EU settlement scheme in Bedford by the end of March, according to Home Office figures.
This was 1,800 more than the 19,060 who had been successful by the end of December, when the Brexit transition period ended.
EU citizens who have lived in the UK for at least five years, and meet certain criteria, can receive settled status and remain in the country indefinitely if they apply by June 30.
Those who have lived in the country for less time can obtain pre-settled status, and the chance to reapply for settled status once they have done so for five years.
In Bedford, 12,320 applications had been granted settled status by March 31, and 8,540 pre-settled status – with 810 applications either refused, withdrawn or deemed invalid.
The EU Rights and Brexit Hub, a legal research facility at York University, say this month's hard deadline is not necessary, and represents an "imminent timebomb".
Professor Charlotte O'Brien said: "The universal rule of deadlines is that people will miss them.
"Those who miss the deadline will become, overnight, unauthorised or illegal migrants, subject to a hostile environment and possible removal.
"It means they will go from being lawful, in many cases long-term and economically contributing EU citizens, to people who cannot lawfully work, rent, or even drive a car."
She added that guidance for caseworkers dealing with late requests was not sufficiently clear and may trigger a "late application lottery".
In Bedford, the highest number of applications were submitted by people from Poland (6,720), followed by those from Romania (4,840) and Italy (2,730).
Across the UK, 385,000 people applied to the EUSS between January and March – down from 855,000 in the three months to December, and 713,000 during the first three months of last year.
The Migration Observatory at the University of Oxford said economic turmoil and the coronavirus lockdown in January – coinciding with the introduction of the post-Brexit immigration system – impacted visa applications to the UK.
Madeleine Sumption, director of the organisation which analyses immigration and migration issues affecting the UK, said: “Covid has had an extraordinary impact on migration, and low migration from EU countries is one consequence of that.
"In fact, there’s evidence that net migration from EU countries was actually negative last year.
"Add to that the impact of a more expensive and restrictive visa system for EU citizens and it makes sense that not many have come under the post-Brexit immigration rules.”
Kevin Foster, minister for future borders and immigration, said if an EU resident has "reasonable grounds" for missing the deadline, they will be given further opportunity to apply.
He added: "The Home Office has also made up to £22 million available in funding for a network of 72 UK organisations to help vulnerable people apply the scheme, and has invested nearly £8 million in marketing campaigns to encourage people to apply to the EUSS."