The latest Office of National Statistics (ONS) released today showed there was an increase of 154,000 from the previous three months and up 584,000 on the same period a year earlier.
There was also a decrease in the number of people claiming job seekers allowance in January 2013 compared with January 2012.
Overall, the ONS said there were 29.73 million people in the UK in employment, of which 73% were working full-time and 27% were working part-time.
In the three months to December, the unemployment rate fell to 7.8% - down from 7.9% in the previous quarter.
But youth unemployment increased by 11,000, the highest rise for a year, and the number of people with more than one job increased by 41,000 to 1.1 million.
The ONS also reported a continued cut in the real value of pay, with average earnings increasing by 1.4% in the year to December, down by 0.1% on the previous month.
Stephen Barter, director, KPMG Management Consulting, said: "We have now seen more than two successive quarters of falling unemployment and this is an encouraging sign for the long-term outlook of the economy and of employers' intentions for future employment growth.
"Of course, on its own, a figure showing a drop in the number of claimants is not a silver bullet, but taken alongside other positive economic data, such as house prices and stock prices, it is an encouraging trend."
Tom Hadley, director of Policy and Professional Services said: "Employer confidence remains strong and the outlook for the UK labour market in 2013 is generally very positive, although there are still legitimate reasons to worry about persistent levels of youth unemployment.
"The private sector continues to overcompensate for public sector job losses and in some high demand areas starting salaries are inflating as businesses find themselves in a race for talent.
"When skills shortages emerge employers need to be flexible. Business demand for candidates in highly skilled areas like engineering, IT and management is outstripping the UK's current supply of qualified and experienced candidates."
Hadley added: "Bosses need to think about whether they could do just as well by taking on someone who shows potential if they can't find candidates with the years of experience they might initially feel are necessary for a role.
"That change in attitude would also be good news for graduates and younger jobseekers."
