The findings are the major surprise in the latest Recruitment and Employment Confederation and KPMG Report on Jobs.
The report found increases in permanent and temporary staff appointments during July hit a nine-month low across all industries.
But construction and engineering out-performed all other sectors as vacancies continued to increase strongly.
Bernard Brown, Partner and Head of Business Services at KPMG said: “The UK job market continued to slow down in July with overall demand for staff rising at the slowest pace in eight months.
“Surprisingly, engineering & construction is the sector where staff were most in demand.”
Construction and engineering was languishing at the bottom of the report’s league tables for demand for staff by sector this time last year.
But it has shot to number one for both permanent and temporary staff beating industries like IT and accounting.