The ONS said the unemployment rate rose to 5.6 percent from 5.5 percent in the three months to April as the number of people in employment fell by 67,000, driven by lower numbers of people in part-time work.
It was the first time that the unemployment rate rose since early 2013, shortly before Britain's economy started to recover strongly from the after-effects of the financial crisis.
Economists have previously said they expected the strong pace of job creation in Britain to slow.
A survey published earlier this month by a group representing recruiters found companies were pushing up starting salaries for new hires in response to a lack of suitable candidates for their vacancies.
An ONS official said he was unable to comment on whether the rise in unemployment and the fall in employment was related to Britain's national elections held on May 7.
Wednesday's data suggested the labour market remained weaker than in previous months in June when the number of people claiming unemployment benefit rose by 7,000.
It was the first increase in that measure of unemployment since October 2012.
The outcome of the May elections had looked too close to call in the run-up to polling day but resulted in a clear win for Prime Minister David Cameron and his Conservative Party, removing a big element of political uncertainty for many firms.
Total average weekly earnings in the three months to May, including bonuses, rose by 3.2 percent compared with the same period a year earlier, speeding up sharply from 2.7 percent in the three months to April.
It was the biggest increase in total pay over a three-month period since April 2010, the ONS said.
Excluding bonuses, pay rose by 2.8 percent, the biggest increase in more than six years.
Economists taking part in a Reuters poll had forecast total earnings would rise by 3.3 percent and that earnings excluding bonuses would increase by 3.0 percent.
The Bank of England is keeping a close eye on wages as it considers when to start raising interest rates from their record low of 0.5 percent.
BoE Governor Mark Carney said on Tuesday that earnings data up to April had been a touch firmer than the central bank expected.
The recovery in earnings and near-zero inflation is boosting the spending power of British households after their living standards worsened over the past five years when pay growth lagged inflation.
Consumer prices were unchanged in the 12 months to June, the ONS said on Tuesday.
Finance minister George Osborne announced last week the introduction of a new, higher minimum wage.
Wednesday's data showed pay, including bonuses, rose 2.6 percent on the year in May alone, slower than a 2.7 percent rise in April. Excluding bonuses, pay rose 2.7 percent.
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