Around 314,000 redundancies were registered during the three months, up by 181,000 from the quarter before, according to the Office for National Statistics (ONS).
The data suggests that unemployment in the UK reached 4.8% in the three months to September.
It is an increase of 0.7 percentage points on the quarter before, and 0.9 percentage points from a year ago.
Meanwhile, around 33,000 people were dropped from payrolls last month, adding to the 782,000 reduction in payrolls since March this year, when the pandemic struck.
ONS deputy national statistician for economic statistics Jonathan Athow said: “The latest monthly tax numbers show over three quarters of a million fewer employees on the payroll in October than in March.
“Unemployment grew sharply in the three months to September, with many of those who lost their jobs earlier in the pandemic beginning to look for work again. The number of redundancies has also reached a record high.
“Vacancies continued to recover from the very low numbers seen earlier in the year. However, these figures predate the reintroduction of restrictions in many parts of the UK.”
Since the figures were taken, several parts of the country have re-entered various stages of lockdown, including severe restrictions in England, which were put in place last week.
As a result, the Government decided to extend its furlough scheme until March next year, ensuring that employees who cannot work will get up to 80% of their salaries.
Suren Thiru, the head of economics at the British Chambers of Commerce, said: “While there was a rise in the number of job vacancies, this is more likely to reflect a temporary bounce as the economy reopened before recent restrictions were reintroduced, rather than a meaningful upturn in demand for labour.
“The extension to the furlough scheme will safeguard a significant number of jobs in the near term. However, with firms facing another wave of severely diminished cashflow and revenue and with gaps in Government support persisting, further substantial rises in unemployment remain likely in the coming months.”
He called for more grants for businesses that have been hurt by restrictions, and asked the Government to ensure that it closes gaps in its support schemes, including for unemployed people.