The UK's unemployment rate remained at 4.9%, the Office for National Statistics (ONS) said.
According to the ONS, the number of people on the claimant count in July, the first month since the Brexit vote, was 763,600, down 8,600 from June.
Wages excluding bonuses rose 2.3% in the three months to June compared with a year earlier, the ONS said.
Including bonuses, earnings growth was 2.4%.
"The labour market continued on a strong trend in the second quarter of 2016, with a new record employment rate," said ONS statistician David Freeman.
"However, little of today's data cover the period since the result of the EU referendum became known, with only claimant count and vacancies going beyond June - to July for the former and to May-July for the latter," he added.
The jobless total is now at its lowest for eight years, while the unemployment rate is at its lowest since the summer of 2005, according to the ONS figures.
The employment rate reached a record high of 74.5%, with 31.8 million people in work in the three months to June - 172,000 more than the previous quarter.
Brexit 'labour market toll'
Howard Archer of IHS Global Insight said that the UK economy showed "impressive resilience in the run-up to the EU referendum and the immediate aftermath of the vote to leave".
However, he warned: "It is premature to draw any firm conclusions from this... It remains likely that softening economic activity and heightened uncertainty will take a toll on the labour market over the coming months."
Hargreaves Lansdown economist Ben Brettell said that while forward-looking surveys to gauge business confidence had suggested the Brexit vote had delivered a shock, "surveys are driven by sentiment, and can therefore overreact".
"The dramatic fall in confidence may not ultimately be borne out by activity, and today's claimant count number is a tentative sign that things might not turn out as bad as many predicted," he said.
Anna Leach, head of economic analysis and surveys at employers' organisation the CBI, said that before the Brexit vote, "the UK's jobs market remained in rude health, though vacancies have continued to tick down since the beginning of the year."
She said the Bank of England had been right "to act swiftly to shore up confidence and keep money flowing through the economy" by taking steps such as lowering interest rates.
She called on the government to "make ambitious decisions in the Autumn Statement that will secure the UK's economic future as changes to trade, regulation and access to skills loom on the horizon".
Suren Thiru of the British Chambers of Commerce said: "Labour market indicators tend to lag behind the wider economy, so it is likely to be some time before the full post-referendum employment picture emerges.
"However, more needs to be done to boost business confidence, so that firms can continue to grow and recruit."
Source: BBC - http://www.bbc.co.uk/news/business-37105028
Posted on Wednesday Aug 17