The jobless total fell by 99,000 in the three months to November to 1.6 million.
This week's raft of job losses in the steel industry will not feed through for months.
Tata announced more than 1,000 redundancies on Monday, while Sheffield Forgemasters said on Wednesday that 100 jobs are set to be cut from its 700-strong workforce.
The official data from the Office for National Statistics (ONS) showed that unemployment has fallen by 239,000 over the past year.
The claimant count has also fallen - down by 4,300 last month to 785,900, the lowest since March 2008.
Employment has reached a record 31.3 million, a rate of 74%, increasing by more than half a million over the past year and by 267,000 in the latest quarter.
Almost 23 million people are in a full-time job, 436,000 more than a year earlier, while 8.4 million are working part-time, up by 152,000. The number of workers in part-time jobs wanting a full-time post is 1.2 million, down by 21,000 in the latest three months.
Economic inactivity, counting people on long-term sick leave, looking after a relative or who have given up looking for work, fell by 93,000 to just under nine million, the lowest since the spring of 2014.
The inactivity rate for women reached a record low of 27%. The record high was 44% in 1971, when most employment records started.
Average earnings increased by 2% in the year to November, down by 0.4%.
Other figures showed that job vacancies have increased by 13,000 to a record high of 756,000.
ONS statistician David Freeman said: "These results show the labour market continued to strengthen in the autumn.
"The employment rate, at 74%, was the highest on record, as was that for women, while the rise in the number of people in work - 276,000 on the quarter - was the third highest on record.
"Real earnings continued to grow, albeit at a slower pace than in mid-2015."
Employment Minister Priti Patel said: "This is a record-breaking set of figures and has got 2016 off to a fantastic start.
"There are now more people in work than ever before and wages are growing - a credit to hard-working Brits and businesses alike.
"And in a further demonstration of the strength of the UK labour market, today's figures show there are a record three-quarters of a million vacancies.
"We will build on this throughout the coming year - doubling childcare for working parents and introducing the new National Living Wage - ensuring that everyone has increased financial security and the opportunity to get on and succeed in life."
Prime Minister David Cameron said: "Unemployment is now below where it was before the recession. We must stick to our plan to keep delivering jobs and security for people."
A Welsh Government spokesman said: "Over the last year Wales has seen the joint largest reduction in the unemployment rate of anywhere in the UK - down 22,000.
"However, this week's Tata announcement has been a stark reminder of the challenges to Wales in a global market.
"Later today the Business Minister is chairing a high-level taskforce charged with drawing up an action plan to support the workforce and the local supply chain.
"The Welsh Government has a strong relationship with industry in Wales, working in close partnership over many years. We will continue working tirelessly to provide support during this challenging time."
During Prime Minister's Questions, Mr Cameron said the unemployment rate was now lower than at the start of the recession.
"Over the last year we have actually seen more people in work in every region in our country and that is something that is welcome," he said.
"The latest figures show unemployment falling by another 99,000 and we have today in our country a record number of people in work ever in our history and a record number of women in work," he added.
"Since I have become Prime Minister 2.3 million more people in work."
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