There were 2.28 million EU nationals working in this country in the quarter to June, 86,000 fewer than a year earlier, the largest annual decrease since records began in 1997.
Unemployment fell by 65,000 in the latest quarter to 1.36 million, the lowest figure since 1976, giving a jobless rate of 4%.
In Yorkshire, the rate of unemployment is slightly above the national average, at 4.2 per cent.
But the total number unemployed has fallen by 12,000 in Yorkshire, to a total of 114,000 for April to June 2018 compared to the previous quarter.
The number of people in work continued to increase - up by 42,000 to 32.39 million, although the rate remained at 75%, said the Office for National Statistics.
Job vacancies increased by 20,000 to a record high of 829,000, while average earnings increased by 2.4% in the year to June, down from 2.5% the previous month.
The number of workers on zero-hours contracts fell by 104,000 over the past year to 780,000, the first substantial fall since the ONS started tracking the figures in 2000.
The percentage of workers employed on a zero-hours contract is now 2.4%, down from 2.8% a year ago.
Senior ONS statistician Matt Hughes said: "The number of people in work has continued to edge ahead, though the employment rate was unchanged on the quarter.
"The growth in employment is still being driven by UK nationals, with a noticeable drop over the past year in the number of workers from the so-called A8 eastern European countries in particular."
The number of people classed as economically inactive, including students, those on long-term sick leave, taken early retirement or who have given up looking for work, increased by 77,000 to 8.7 million in the latest quarter, giving a rate of 21.2%
The claimant count, which includes people on Jobseeker's Allowance and theunemployment element of Universal Credit, increased by 6,200 last month to 906,100, almost 108,000 more than a year ago.