The total fell by 21,000 to 1,459,000 during the three months to December.
The UK jobless rate edged lower to 4.9% - the joint lowest level since records began in 1984 - the Office for National Statistics (ONS) reported.
Meanwhile, the number of people out of work and claiming unemployment benefit fell last month by 13,400 to 892,100 - the lowest total for almost 30 years.
Under the claimant count measure, which has fallen for eight consecutive months, the UK jobless rate dropped to just 2.9%. 'Healthy outlook'
Growth in earnings unexpectedly slowed again, according to the ONS.
Average earnings increased by 3.4% in the final quarter, down a touch from 3.5% in the three months to November.
But economist Howard Archer of Global Insight said Britain's labour market remained buoyant.
"The current strength in economic activity, and relatively healthy outlook, suggests that the labour market will tighten modestly further over the coming months," he said.
He added that the relatively contained earnings figures would limit "the pressure on the Bank of England to tighten monetary policy aggressively over the coming months". BBC News