UK unemployment fell by 13,000 between September and November to stand at 1.65 million, government figures show.
Analysts say the strength in labour market is unlikely to continue
The Office for National Statistics (ONS) said the number of people claiming jobseeker's allowance in December fell by 6,400 to 807,700.
This was the lowest number since 1975 and the 15th consecutive monthly fall in the number of claimants.
Analysts said the data suggested the UK job market remained robust despite expectations of an economic slowdown.
"UK labour market data for December showed that the increasing doom and gloom on the economy is not yet hurting the labour market," said Alan Clarke at BNP Paribas.
However, there are worries that the strength in the labour market may fade as growth slows.
"Ultimately, the labour market lags activity and survey indicators are already pointing to a standstill in hiring growth," Mr Clarke added.
Average earnings growth remained unchanged at 4% in the three months to November although economists had forecast the rate to ease to 3.9%.
Excluding bonuses, earnings growth was 3.6%.
While the data was unlikely to change expectations for a cut in UK interest rates in February, analysts said it could mean any further reductions would be slower in coming.
At the same time, the number of working pensioners has hit a new record, up by 6.5% to 1.26 million over the last year.
Working pensioners are now the fastest-growing age group within the working population, says BBC employment correspondent Martin Shankleman.
Chris Ball, of the Age of Employment Network, called the trend "significant" and predicted the totals would climb higher.
"We estimate that perhaps double the present number working want, or need, paid work," he said, "not just to pay for life's little luxuries, but for the basics of food, fuel and lighting."
But he said older people were still victims of discrimination which made it lawful to fire people once they reached 65 years old, which he said was "an absurd waste of fit and able people".
Figures show the number of working pensioners - men over 65 and women over 60 years of age - has doubled this decade. In 2000, there were a total of 827,000.
"It may be because of difficulties over pensions, decline in final salary schemes, but fundamentally people want to work longer, there is a desire for that," said Tony Maltby, a fellow at the Centre for Research into the Older Workforce.