The total jobless count sat at 2.51 million in the quarter, according to the Office for National Statistics (ONS).
Meanwhile, the number of people claiming Jobseeker’s Allowance last month fell by 21,200 to 1.48 million.
It was the fastest rate of fall in three years. Total unemployment was at the lowest level since last autumn.
The ONS added that average earnings increased by 1.7% in the year to May, 0.2% up on the previous month.
However, long-term unemployment has increased to a 17-year high, despite the fall in the number of people claiming Jobseeker’s Allowance.
Some 915,000 people have been out of work for more than a year, an increase of 32,000.
Vacancies were up by 24,000 to 529,000, the highest since the autumn of 2008.
Just over 460,000 people have been jobless for more than two years, the highest figure since 1997.
The number of people classed as economically inactive also increased in the latest quarter, up by 87,000 to 9.04 million.
The figure included a 44,000 increase in economically inactive students, a 26,000 rise among the long-term sick and 8,000 more people who retired early.
The ONS also reported that 29.7 million people were in employment in the three months to May, up 16,000 on the previous quarter, and an increase of 336,000 on a year ago.
Unemployment is 72,000 lower than a year ago, with a jobless rate of 7.8%.
Youth unemployment fell by 20,000 to 959,000, giving a jobless rate for 16 to 24-year-olds of 20.9%.
Average earnings increased by 1.7% in the year to May, up by 0.2% on the previous month, giving an average weekly wage of £476.
Full-time employment increased by 28,000 to 21.6 million, but the number of part-time workers fell by 12,000 to 8.04 million.
The number of self-employed people fell by 28,000 to 4.1 million.
Source: Sky News