Despite falling unemployment, wage growth is weak because the supply of labour has also gone up, says the Chartered Institute of Personnel and Development (CIPD).
The CIPD said for every low-skilled job, there were 24 applicants.
There were also 19 candidates for every medium-skilled job and eight for every high-skilled vacancy.
The CIPD's quarterly Labour Market Survey of employers, carried out in association with the Adecco Group, said the workforce had been boosted by more workers from other EU countries, as well as by older workers and former welfare claimants.
The report's author, Gerwyn Davies, who is senior labour market adviser at the CIPD, said pay had been expected to rise along with employment, but such predictions were "the dog that hasn't barked for some time now".
"We are still yet to see tangible signs of this situation changing in the near term," he added.
"The facts remain that productivity levels are stagnant [and] public sector pay increases remain modest, while wage costs and uncertainty over access to the EU market have increased for some employers.
"At the same time, it is also clear that the majority of employers have still been able to find suitable candidates to employ at current wage rates, due to a strong labour supply until now."
Not all recent surveys back up the CIPD's view. Last week, a survey of employment agencies found that the UK labour market was tightening, with employers finding it harder to recruit staff.
The survey, carried out by market research firm Markit for the Recruitment and Employment Confederation (REC), said that pay rates for both permanent and temporary staff were rising quickly because of a continuing fall in the number of job applicants.
Markit said last year's Brexit vote was also driving some EU nationals home, making it harder to fill a wide variety of jobs.
Pressure on incomes looks set to continue, with pay rises forecast at 1% over the next year, a survey predicts.