Oxford University’s Migration Observatory and think tank British Future have warned that new immigration rules could hit social care and hospitality businesses in the UK.
Home Office figures reveal that by the end of September 2020, 19,270 people successfully applied to continue living in the area after December 31.
European Union nationals wishing to continue living in the UK must apply under the EU Settlement Scheme by June 30 2021.
Those who have lived in the UK for five years and meet the criteria, can receive settled status and remain in the country indefinitely.
Those who have lived in the country for less time can receive pre-settled status, which allows them to remain for a further five years. They can later apply for settled status.
Madeleine Sumption, director of the Migration Observatory, said: "The UK has certainly become less attractive to EU migrants since the 2016 referendum: over the past three years, EU immigration has fallen substantially.”
Of 19,920 applications dealt with in Sheffield between August 2018 and September 30 2020, 10,950 granted applicants settled status and 8,320 pre-settled status.
Around 660 applications were either refused, withdrawn, or invalid.
Figures are rounded to the nearest 10.
In Sheffield, the highest number of applications was submitted by residents from Slovakia (4,610), followed by people from Poland (3,060) and Romania (2,490).
There were also around 970 applications from people who are not from the European Economic Area, but qualify for the scheme. Those qualifying include family members of EU citizens living in the UK.
Across the UK, 3.9 million applications have been made under the EU Settlement scheme since it was launched – 56 per cent of applicants received settled status, 41.6 per cent pre-settled and only 0.4 per cent were refused.
Across the UK the highest number of applications come from residents originally from Poland with 750,000, followed by people from Romania with 640,000, and Italy with 390,000.