The unemployment rate had stood at 5.0 per cent in the three months to April, which had been a near 11-year low, the Office for National Statistics said in a statement.
The ONS added that the unemployment total dropped to an eight-year low of 1.65 million people in the three months to May.
However, none of the data covers the period following Britain's surprise EU exit referendum that was held on June 23.
Bank of England governor Mark Carney has warned that Britain could fall into recession as businesses delay new projects and cut jobs because of the Brexit vote.
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