Starting salaries and temporary staff wages have risen at the sharpest rate for 24 years, a survey suggests.
Robust demand for staff is being fuelled by rising economic activity, said KPMG and the Recruitment & Employment Confederation (REC).
At the same time, there are fewer candidates for jobs, driving big increases in starting pay.
There is strong demand for jobs in sectors including IT staff hotels and catering.
A survey of 400 recruitment firms found the number of people available for jobs has fallen to a near-record low.
Recruiters said greater demand for staff, a high employment rate, fewer EU workers and a lack of confidence among employees to switch roles due to the pandemic all contributed to the latest decline in candidate numbers.
Neil Carberry, chief executive of the REC, said: "We have all seen how labour shortages have affected our everyday lives over the past few weeks, whether that's an empty petrol station or fewer goods on supermarket shelves.
"The scale of the shortages we are seeing cannot be explained by one factor alone, but are a major challenge to businesses' ability to drive the prosperity of the UK in the months and years to come."
"It is essential that government works in partnership with business to deliver sustainable growth and rising wages, rather than a crisis-driven sugar rush," he continued.
Claire Warnes from KPMG, said the "unprecedented increase" in starting salaries is being "driven by the near record fall in candidate availability".
"Wage growth alone is unlikely to help sustain economic recovery because of limited levers to bring people with the right skills to where the jobs are and increase productivity," she added.
'Competition is fierce'
While she noted that the sharp rise in hiring activity is a "reason to be hopeful", she added that "competition is fierce" because many workers do not have the skills needed to transfer to the sectors with most demand.
"Reskilling and supporting people to move jobs which are in demand needs to be speeded up. Otherwise we may see these clear tensions in the labour market turning into a workforce crisis in many sectors," she added.
International recruiting firm, Robert Walters Group, which operates in areas including the UK, Asia and Australia also said that "competition for talent is fierce" at the moment.
Robert Walters, chief executive officer at Robert Walters Group, which recruits for jobs such as lawyers, accountants, IT professionals told the BBC's Today programme on Thursday that "there are shortages in pretty much any country you care to name".
The firm has put up its profit forecast for the year.
Mr Walters said that skills are more in demand as "every job is getting more complicated".
Sectors such as law and accounting are also experiencing greater demand, according to his data, and he said the company is now seeing law firms pay newly qualified lawyers £150,000 per year or more, which he added is "unheard of".
'Significant' wages increases
"We're seeing wage inflation of 20% upwards... We've had cases of 100% so it's significant," he added.
Next chief executive Lord Wolfson warned this week that warehouse and logistics staffing is under pressure.
He said the retailer was struggling because staff are not available in the places needed and seasonal workers were difficult to recruit.
Lord Wolfson called for businesses to be able to get visas for skills they "desperately need" and recommended that they should have to pay UK workers the same amount as overseas workers.
To make this competitive, he argued businesses should have to pay a "visa tax on top - lets say 7% of wages".
At Next, Lord Wolfson said that warehouse wages had gone up by around 60% in the last ten years and 70% for Christmas wages, and added that "wages have already gone up significantly".
But, he said the firm was still finding that there were not enough workers in particular areas who wanted to move for short periods of time.
The most recent figures from the Office for National Statistics suggested that growth might be stalling, with real wages - a measure that takes account of rising prices - looking lower in July than they were in April.
There was also a jump in inflation reported for August as well as rising energy prices.
Average earnings fell in the first months of the pandemic as people were furloughed, which meant in many cases their pay fell, or they worked fewer hours.
The annual figures we are now seeing are compared with early in the pandemic, which is making the increase in wages bigger.
Throughout the pandemic, more low-paid employees have lost their jobs than high-paid employees, which means that average earnings have gone up.
There are also 2.6 million workers affected by the public sector pay freeze who will not benefit from rising wages according to the Resolution Foundation.