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Overall job vacancies increased at the strongest rate in six years last month, and the number of vacancies for permanent positions increased at the sharpest rate since March 2010.
In addition, starting salaries rose at the fastest rate in 26 months. "This is an early indicator of increased competition for candidates and skills shortages in a growing number of sectors," said Kevin Green, chief executive of the Recruitment and Employment Confederation.
"We anticipate starting salaries increasing over the coming months as the economy strengthens and competition to secure talent hots up."
A string of better-than-expected economic indicators in recent weeks have raised hopes the U.K.'s economy is reviving, after two years of stagnation. This week alone has seen upbeat data for the retail and housing sectors, and the highest PMI (purchasing managers' index) reading for the service sector in nearly 7 years.
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While optimistic about the overall improvement in the economy, Bernard Brown, the head of business services at KPMG, said the uptick in job vacancies could also reflect a labor market skills shortage.
"A gap exists between the demand for staff and the quality of candidates available, so the onus is on candidates to improve their skills and prove their capability," Brown said in the KPMG report.
He added that a more vibrant labor market could mean employers have to work harder to retain staff.
"For some time, staff have sat tight, refusing to move when job security was low. Now the best staff will be looking for better offers so employers will need to strike a balance between recruiting new blood and retaining their best employees," Brown said.
At his first press conference on Wednesday, the new Bank of England Governor Mark Carney said the central bank would keep interest rates at record lows until unemployment falls to 7 percent or lower.
According to official estimates, unemployment stood at 7.8 percent between March and May, down 0.3 percent from a year earlier. The Office for National Statistics will release its latest estimate next Wednesday.
—By CNBC's Katy Barnato