David Cameron has hailed news that Britain’s employment rate is at the joint highest level since records began in 1971 as evidence that the economy is strengthening.

Speaking at the Rolls Royce car factory in Goodwood, Sussex where the luxury car firm has just announced plans to build an SUV, Cameron said: “I’m not saying we have solved all our problems in the British economy in the last four and a half years, but we are on our way.”

Employment increased by 103,000 in the three months to December, according to the Office for National Statistics (ONS), driving the employment rate to 73.2%, as the economy continued to grow.

The ONS said that this figure was higher than the pre-crisis peak of 73%, recorded in early 2008, and has only been matched once, in 2005, since records began more than 30 years ago.

The prime minister has said he wants to create full employment, and the latest rise will boost his hopes of stoking a feelgood factor in the runup to the general election in May.

The ONS pointed out that the record employment rate for women, at 68.5%, partly reflected the increase in the state pension age, “resulting in fewer women retiring between the ages of 60 and 65”.

Unemployment fell by 97,000 over the three-month period to 1.86 million, the ONS said, and average wages rose at the fastest pace since mid-2013. The unemployment rate continued to decline, to 5.7%.

Measured on the claimant count, which only includes the number of people in receipt of out-of-work benefits, unemployment also fell, by 36,300 in the month to January, to 843,100.

Average pay including bonuses was up by 2.1% on an annual basis, the ONS said. With inflation running at an annual rate of just 0.5% in December, that confirmed that the long-running squeeze on living standards has come to an end for the time being.

John Philpott, the director of The Jobs Economist, pointed out that without factoring in bonuses, pay growth remained relatively weak, at 1.7%.

“Although the December bonus season pushed growth in total average weekly earnings above 2%, underlying pay pressure as measured by regular average weekly earnings fell slightly.

“This suggests that the jobs rich economic recovery is still failing to boost labour productivity, which does not bode well for long-term improvement in UK living standards, even if very low price inflation is at present helping to raise real incomes,” he said.