The report also indicated starting salaries are on the rise.
The Recruitment and Employment Confederation (REC) and KPMG Report on Jobs provides a comprehensive guide to the UK labour market, drawing on original survey data provided by recruitment consultancies.
The north saw the fastest growth of permanent placements in January, followed by the Midlands. London and the south posted modest increases.
All four English regions posted growth of temp billings during January, albeit at varying rates. The strongest expansion was signalled in the north, whereas midlands-based agencies saw only a marginal increase.
Private sector demand for permanent employees rose at a strong rate in January, with growth picking up to a ten-month high. However, private sector demand for temporary staff dipped slightly for the first time in a year.
In the public sector, demand fell for both permanent and temporary staff in January, with the former recording the sharper decline.
Engineering, construction and IT were the most in-demand categories of permanent staff during January, the report found. It also showed a strong rate of expansion was signalled for staff in the nursing, medical care sector.
The weakest growth was recorded for Hotel & Catering workers.
The report found that nursing, medical care was the most sought-after type of short-term staff during the latest survey period, and by some distance. Engineering, construction and accounting financial workers also saw robust improvements in demand for their services.
Bernard Brown, partner and head of business services at KPMG, said: "Amid the doom and gloom caused by predictions of slow growth, the hiring figures for January should give employers and employees plenty of reasons to be cheerful.
"Demand for staff is at its highest peak for almost two years meaning that employees who may have been too nervous to change jobs in recent months, might consider the benefits of a fresh challenge.
"Given the skills gaps that continue to plague many sectors, increased availability of qualified and experienced staff could help fill the capability gap many employers have wanted to plug for some time."
REC director of policy and professional services Tom Hadley said: "The war for talent has begun. January saw the sharpest rise in starting salaries in well over a year after a nine-month trend of increases.
"The rise is caused by continued growth in permanent vacancies paired with a reduction in candidate availability. This is good news for workers but also highlights the need to address the current 'skills disconnect', which presents a major barrier to growth in key sectors of our economy.
"Skills shortages in whole sectors like engineering and IT and for particular roles like chefs, drivers and sales are spurring competition for qualified staff. Employers are realising that to secure the talent they need they have to offer more attractive salaries."