The rate of unemployment in the UK remained at 4.9% in the three months to June, according to the Office for National Statistics (ONS).
The number of people out of work fell 51,000 to 1.64 million. The second quarter saw the number of people in work rise to another record of 31.75 million.
The figures also show that unemployment actually fell in July alone, despite expectations that it would increase following the vote to leave the European Union.
The number of people claiming jobseekers' allowance fell 8,600 to 763,600 people in July, following a 900 increase in June.
The ONS said wages, excluding bonuses, were up 2.3% in the three-month period. And following recent inflation data, that means workers saw a real-term wage increase of around 1.5%. However, that could be short lived.
Following Tuesday's inflation figures, Jeremy Cook, chief economist at World First, said he expects inflation to "spike above 2.5% next year". And with the growth of wages likely to slow down towards the end of this year and into 2017, workers will start to see their wages, in real terms, get squeezed.
What happens when we start seeing our bank balance a little tighter? We spend less, don't we. We prepare for the worst case scenario. We don't want to be left short if the car needs to go to the garage, or the boiler breaks down, or the children need new trainers. That means less money being spent with businesses; retailers, restaurants, hotels, activities - all part of the UK's vital services sector, which accounts for around 75% of the entire British economy.
Scott Bowman, UK economist at Capital Economics, described wage growth as "subdued". He said: "Earnings growth is still subdued considering how much the labour market has tightened in recent times. What’s more, the vote to leave the EU should cause some firms to put hiring decisions on hold or cut back headcounts altogether, resulting in the unemployment rate drifting up over the coming quarters. This should contain any further rises in earnings growth and keep domestic cost pressures in check.
"Accordingly, the Monetary Policy Committee should be able to follow through with more monetary easing in order to support the economy, without worrying about stoking domestically-generated inflation too much."