Less than two per cent of newly-hired staff at Lincolnshire Community Health Services Trust are from the EU, figures reveal.
But healthcare workers' union Unison has warned that a lack of European employees would lead the NHS to 'a state of near collapse'.
Between December 2017 and November 2018, the equivalent of 165 full-time workers started at the Lincolnshire Community Health Services NHS Trust, NHS Digital data shows.
The three joiners from the EU made up 1.8 per cent of the intake, with 91% from the UK.
Across England, EU citizens made up 7.5 per cent of people joining the NHS over the same 12 months.
Sara Gorton, Unison's head of health, said hospitals were finding it harder to recruit and retain EU staff in the midst of uncertainty around Brexit.
She said: "Without the many health employees from across Europe, the NHS would be in a state of near collapse.
"Their skills and expertise have helped limit the effects of the huge staffing gaps.
"Staff losses would mean even more stress for an already overstretched workforce, and would have a devastating impact on patient care."
Across England, fewer EU nationals are joining the NHS and more are leaving than before the referendum, while the trend is reversed for staff from the UK.
The number of EU citizens starting full-time jobs has fallen by 26 per cent, from 14,500 in 2014-15 to 10,800 in 2017-18, while the number leaving work has risen from 6,700 to 9,600.
Conversely, 109,000 full-time UK workers joined the NHS in 2017-18, compared with 103,000 three years earlier.
The Department of Health and Social Care said it was encouraging NHS workers from the EU to apply for settled status.
A spokesperson said: "EU workers play a vital role across the health and social care system, and we want them to stay here long after the UK leaves the EU.
"Our priority is to make sure that high standards are maintained across the healthcare system, and that patients continue to receive the high-quality care they deserve."