The number of unemployed dropped to 2.49 million in the three months to July, helping nudge the jobless rate to 7.7% from 7.8%, figures from the Office for National Statistics (ONS) showed.
That drove the pound to a seven-month high against the dollar as markets cast doubt on Bank of England governor Mark Carney's new "forward guidance" policy, which pegs rate rises to unemployment.
The so-called claimant count - the number claiming jobseeker's allowance - fell by 32,600 in August to 1.4 million.
July's claimant count was also revised lower, and the combined 68,900 fall in claimants in July and August was the biggest two-month drop since June 1997.
The Government insisted the economy is "turning the corner" as the number of people in work increased by 80,000 in the quarter to July, rising to 29.84 million, hitting another record high as the population continues to swell.
But the continued squeeze on household incomes was highlighted by a 1.1% increase in average weekly earnings between May and July versus a year earlier. Pay continues to lag behind inflation, which is running at 2.8%.
And areas such as the North East and North West continued to see unemployment rise - up 5,000 and 13,000 respectively compared with the previous quarter.
By contrast, there were declines of 29,000 in the South East and 7,000 in London. Unemployment also fell in the East Midlands, the South West, Wales and Northern Ireland.
The North East has UK's highest jobless rate at 10.4%, compared with a 5.8% unemployment rate in the South East.
The figures also showed continuing pressure on the public sector, where the number of workers fell 34,000 in the three months to June to 5.67 million. The total public sector workforce has fallen 104,000 on a year earlier.
Private sector workers rose 114,000 in the quarter to July, hitting 24.17 million, and have increased 380,000 over the year.
Youth unemployment also remains stubbornly high, with the number of jobless 16 to 24-year-olds rising by 9,000 in the three months to July to hit 960,000.
Employment Minister Mark Hoban insisted: "This is a really encouraging set of figures, with the number of people in work rocketing by 80,000 in only three months - a rise driven entirely by a growth in full-time jobs.
"The private sector has created jobs for 1.4 million more people under this Government, and there are now more people employed in the private sector than ever before."
But TUC general secretary Frances O'Grady said: "Despite the Chancellor's boasts this week, austerity is continuing to cause damage and we are far from a strong and sustained jobs recovery.
"While the headline figures show small improvements, youth employment has fallen sharply and long-term unemployment is still rising. There are also still record numbers of people trapped in involuntarily part-time work, with underemployment continuing to soar.
"Across the economy ordinary people are yet to feel the benefits of tentative growth, with wages rising around three times slower than prices."
The unemployment rate has taken on new significance after the Bank said it will not consider raising interest rates from their record low until it falls to 7% - which it forecasts will take around three years - barring a spike in inflation.
Borrowing costs have been rising as markets speculate the Bank will lift rates sooner.
Martin Beck, UK economist at Capital Economics, said the jobs market appears to be "fully sharing in the economy's momentum". But he said with plenty of scope to improve productivity, it should take a long time for the jobless rate to fall to 7%.
He said: "Although employment rose strongly, more timely evidence from the recent activity surveys suggests that firms are responding to higher demand more by boosting productivity than taking on new workers."
Kathleen Brooks, UK research director at Forex.com, added that the Bank " may not be losing too much sleep" as the jobless statistics show pockets of weakness.
David Kern, chief economist at the British Chambers of Commerce, said the figures show that the private sector is driving the recovery.
"While it is concerning that there were increases in youth unemployment and the long-term unemployed, it is pleasing that the number of those claiming benefits continues to fall," he said.