The UK's unemployment rate rose to 4.8% in the three months to September, up from 4.5% as coronavirus continued to hit the jobs market.
Redundancies rose by a record 181,000 in the quarter to reach a record high of 314,000, the Office for National Statistics (ONS) said.
Firms made more workers redundant in anticipation of the end of the furlough scheme, which was originally supposed to finish at the end of October.
It will now last until 31 March.
The number of people out of work rose by 243,000 in the quarter, the largest increase since May 2009.
In particular, there was a big fall in the number of 16 to 24-year-olds in employment over the last quarter, decreasing by 174,000 to a record low of 3.52 million.
"The pandemic continues to bring turbulence to the UK labour market," said Tej Parikh, chief economist at the Institute of Directors.
"In the autumn, employers faced difficult decisions around retaining staff as government support looked set to decline. The initial shape of the Job Support Scheme, originally expected to come into force this month, didn't provide a smooth off-ramp from furlough.
"The extension of the furlough scheme through to March is welcome as it has given directors certainty to plan ahead for their staff. Unfortunately, the change appears to have come too late in the day for some."
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