Regular pay rose by 5.7% in the year to September, the fastest growth since 2000 excluding the pandemic, when people got big rises when returning to work from furlough.
However, when adjusted for rising prices, wages fell by 2.7%.
The cost of living is currently rising at its fastest rate in almost 40 years, largely due to the war in Ukraine.
Energy and food prices have shot upwards, leaving many people struggling to pay their bills.
ManpowerGroup, one of the UK's biggest recruiters, told the BBC that the gap between wages and prices was "putting more and more pressure on households".
The UK unemployment rate rose slightly to 3.6% in the three months to September, up from 3.5% in August, the Office for National Statistics (ONS) said.
However, while this is near a 50-year low, the Bank of England has warned that unemployment will nearly double by 2025 as the UK goes through a tough recession.
On Thursday, Chancellor Jeremy Hunt will set out his plans to get the economy back on track, with spending cuts and tax rises expected.
The Times reported on Tuesday that Mr Hunt and the prime minister will announce a significant rise in the national living wage and target new cost-of-living payments at the poorest households.
Josh Hawker, a director at care home company AbleCare, says the firm has been struggling to recruit for a few months now, despite its overall wage bill rising by 10%,
AbleCare, which runs six care homes around Bristol and South Gloucestershire, is also finding it difficult to retain staff, with carers tempted away by high pay offers outside of the sector that the business cannot compete with.
"I'm getting really fed up with reading resignation letters that say: 'I love my job, I don't want to go, I love looking after the residents but I have to put my family and myself first,'" Mr Hawker says.
"They're getting offers of 20 or 30% higher than we can possibly pay, to go and work at places like Amazon and the big supermarkets. What can you say to them? What can you say other than 'fair enough'?", he says.
The company has done what it can to raise pay, and has started to offer health insurance as an incentive for staff. But facing rising costs, the business has limited room to boost salaries.
Neil Carberry of the Recruitment and Employment Confederation trade group said the latest figures showed the "exceptional growth" in demand for new workers seen this year was at an end.
But he added: "Despite increased levels of employer caution, vacancies are still at historically high levels - it is still a good time to be looking for work. Unemployment remains at record lows, while employment is still below February 2020 levels."
Gareth Vale, director of operations at ManpowerGroup, said falling real-terms wages were hurting households.
"With average total pay... not keeping pace with inflation, some people are looking to work more hours or take on an additional role to supplement incomes to keep pace with rising costs. Employers will need to keep an eye on this in terms of staff wellbeing and the impact it could have on overall productivity and growth."