The report, published today, found temporary and contract staff billings rose from May with the latest increase the strongest in seven years.
REC chief executive Kevin Green said the UK jobs market is in "blast off", with the highest number of people being placed in permanent jobs for two years and demand for staff at a three-year high.
"The UK jobs market has been agile enough to weather the recession and emerge with more people in work than ever and has performed considerably better than our European counterparts," he said.
The report provides a comprehensive guide to the UK labour market, and draws on original survey data provided by recruitment consultancies.
There was also positive news for salaries with permanent staff wages rising at the fastest pace for 23 months in June. Temporary and contract staff pay growth also quickened, reaching the sharpest rate since March 2008.
Regional and sector variations
The south of England posted the fastest rise in permanent appointments, closely followed by the north. The midlands saw a solid expansion, while London recorded a moderate increase.
Public sector permanent vacancies rose for the first time in six months during June, while public sector temporary and contract vacancies were unchanged from May.
In the private sector, both permanent and temporary and contract vacancies increased at the fastest pace since December 2011.
KPMG head of business services Bernard Brown said all the signs point towards an economy an upward trajectory.
"The latest figures reveal permanent placements enjoying their highest growth rates for over two years and temporary roles being filled at the quickest pace since Christmas," he said.
"Perhaps the sun has finally come out to shine on the jobs market and economy at large? Employers seem to think so. Many have stepped up their search for staff with demand for staff accelerating to a three-year high. Confidence is even beginning to show itself with employers prepared to increase the salaries they offer to new employees."
