The numbers of permanent placements fell to their lowest level this August since 2001, KPMG's September Report on Jobs, produced in association with the Recruitment and Employment Confederation (REC) reveals.
Temporary workers were also hit by the declining demand for staff, signalling a further weakening of the jobs market.
Kevin Green, REC chief executive, said: "The deteriorating economy is now having the expected negative impact on the labour market.
"The demand for both permanent and temporary workers is weakening, although it must be remembered this follows a period of unprecedented high demand for staff."
Alan Nolan, director at KPMG, added: "UK employers are continuing to control payroll costs through redundancies and by refusing to take advantage of a growing, but increasingly unused, pool of skilled labour.
"These workers are starting to drift abroad in search of employment, and there is a risk that when the market turns the UK will be left behind by a skills shortage."
Recruiters in the Exeter area cautiously agreed with the findings but said there was not enough local data to support the figures for Devon.
Hannah Ellis Murdock, director at the Really Good Recruitment Company, said: "There has been a fall in demand at all levels but we don't know what the impact will be in this area. Because all of this is happening now, we don't have a lot of information about how the levels are decreasing down here.
"August was particularly quiet although the month is traditionally fairly quiet anyway. September and October are usually much busier and we will have to see what happens.
"The impact has been clearly seen in the construction industry. We have had a lot of CVs from people in that sector and there are fewer companies recruiting.
"However, sales, marketing and accountancy are all still buoyant.
"The other interesting thing that we are seeing in the market is that there is a greater demand for interim managers. Companies are looking for more flexibility and will fill the gaps. Sometimes a placement could be for a couple of weeks but it might be for as long as six months."
As well as showing a fall in recruitment, the report also revealed changes in sector rankings with both executive and IT recruitment rising.
Ed Jessamine, managing director of TLG Recruitment, based in Silverton, said: "It's been a relatively steady summer. But it has been quiet both in terms of new positions and candidates. We will have a better view of the situation in September.
"At the moment we have the double whammy of depression and lack of confidence in the market.
"If people aren't moving, then the industry becomes stagnant. When they are, we're filling the gaps.
"People are being very watchful and don't want to be out of work."