UK unemployment fell by 121,000 to 2.12 million in the three months to May, official figures show.
The figure is the lowest level in nearly six years, according to the Office for National Statistics (ONS).
The rate of unemployment also fell again, to 6.5% from 6.6% in the three months to April.
The number of people claiming jobseeker's allowance last month fell by 36,300 to 1.04 million, the ONS added.
The latest figures also show that more than 78% of men and 68% of women are in work, giving an employment rate of 73.1%.
Prime Minister David Cameron said this was now equal to the record rate of employment set in 2005.
"Today's figures show more people have the security of a job than ever before. Full employment is a key aim of our long-term economic plan," he said.
Wage growth slows
The latest figures show that wage rises including bonuses are at their lowest since 2009, while excluding bonuses average wage increases are their lowest since 2001.
Average wages in March to May including bonuses were just 0.3% higher than a year ago. Average wage rises excluding bonuses rose in that time by 0.7%.
Wage growth has been steadily declining since the first quarter of this year. Between January and March, annual wage growth including bonuses stood at 1.9%.
Official figures on Tuesday showed the consumer prices index (CPI) measure of inflation rose unexpectedly in June to 1.9% from 1.5% a month earlier.
TUC general secretary Frances O'Grady said: "It's good to see unemployment falling, but with pay growth falling to a record low, serious questions must be asked about the quality of jobs being created in Britain today.
"If all the recovery can deliver is low-paid, low-productivity jobs - many of which don't offer enough hours to get by - then it will pass most working people by and Britain's long-term economic prospects will be seriously diminished."
The ONS added that more than 4.5 million people were self-employed, the highest since records began in 1992, after an increase of 404,000 over the past year.
The Bank of England has recently said it may have underestimated the amount of spare capacity in the UK economy by as much as 0.5% of the country's annual economic output.
BBC employment and industry correspondent, John Moylan, writes:
The meagre growth in average earnings is in stark contrast to the upbeat news on jobs.
The 0.3% year on year rise in total pay, which includes bonuses, was the lowest growth rate since 2009.
But according to the ONS the figure was probably distorted/affected by the fact that last year many firms delayed bonus payments to let staff benefit from the lower rate of income tax.
So regular pay, which excludes bonuses, may give a more accurate picture of wage growth. That was up 0.7% on a year earlier, the lowest growth rate since records began in 2001.
The ONS said that reflected low pay growth across a wide range of sectors.
It means pay continues to lag inflation. That's a trend that's been ongoing since 2009 and which is at the heart of what Labour calls a "cost of living crisis".
The figures led trade unions to again highlight concerns about whether the recovery is really delivering for millions of low paid workers.
The Resolution Foundation also pointed out that the average earnings figures exclude the UK's 4.6 million self-employed.
It has estimated that if they were included "the squeeze on wages since 2008 would be more than 20 per cent deeper than the official figures suggest."
Spare capacity most often stems from underinvestment by businesses, either in new technology, new buildings or hiring new staff. It is the Bank of England's way of gauging how far UK gross domestic product is below its potential growth level.
One of the consequences of spare capacity has been that employers have room to keep hiring staff for some time before they have to increase wages to attract scarce workers.
But low wage growth could also impact on consumer spending and may keep interest rates at 0.5% for longer than currently expected.
Robert Wood, UK economist at investment bank Berenberg said: "Wage growth remains extremely weak, but that cannot last much longer with unemployment falling this fast. We look for a Bank of England rate hike in November."
Labour shadow work and pensions secretary Rachel Reeves told the BBC the average wage figures showed there was "most definitely a cost of living crisis in the UK."