Job vacancies increased by 20,000 to a record high of 829,000 as the number of non-EU nationals working in the United Kingdom increased by 74,000 to 1.27 million.
Average weekly earnings for employees in real terms (adjusted for price inflation) increased by 0.4 per cent excluding bonuses and by 0.1 per cent including bonuses, compared with a year earlier.
The ONS said the UK-wide unemployment rate of 4% had not been lower since February 1975, while the number of people aged 16 to 24 looking for work was the lowest since records began in 1992.
The Kingdom's official jobless rate dropped to 4.0% in June, while the claimant count change showed a bigger-than-expected increase. It continues a trend seen since the 2016 Brexit vote.
The total number of unemployed people in the United Kingdom reached 1.36 million that is 65K less than for January to March 2018 and 124K fewer than for a year earlier.
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.
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The mandate to produce a study came after an earlier version proposed to bar the delivery of F-35s to Turkey. The signing ceremony was held at the military base at Fort Drum (New York) on Monday.
According to data released on Tuesday for the second quarter, hourly production increased by 0.4%, leaving productivity with a growth of only 1.5% per year.
However, there are few signs of overall wage increases - wage growth is slowing down to a nine-month low of 2.4% between April and June.
And there's a key factor making the labour market tighter: a net outflow of European Union nationals working in the UK.
Dr Stuart McIntyre, of the Fraser of Allander Institute, an economic think-tank based at Strathclyde University, said Scotland and the United Kingdom were experiencing "historically low levels of unemployment and high levels of employment".
However, Suren Thiru, head of economics at the British Chambers of Commerce, said this now looked to have been a premature move. Economists had expected the rate to remain at 4.2% level.
Yet, the absence of stronger pay growth so far also raises questions about whether the central bank committee's unexpected unanimous decision was justified.