Employers are finding it increasingly difficult to recruit suitably qualified staff, with shortages in construction and engineering now at a "critical" stage, the Recruitment and Employment Confederation (REC) said.
The new National Living Wage of £7.20 an hour next April could also "put the brakes" on jobs growth, a report suggested.
Kevin Green, chief executive of REC, said: "As politicians make their big pitches to workers and to business at the party conferences, the UK jobs market is entering a new phase.
"Talent shortages are making it increasingly difficult for employers to find quality candidates.
"This is now at a critical stage in the construction and engineering sectors, constituting a major threat to planned rail upgrades and housebuilding projects.
"The planned introduction of the national living wage is causing businesses to consider alternatives to hiring more staff and this could lead to greater automation in some sectors."
Permanent placements from recruitment agencies continued to increase last month, but at the slowest rate for two-and-a-half years, REC said.
Starting salaries also increased last month, although the rate of growth fell to a 20-month low.
Mick Cash, general secretary of the Rail, Maritime and Transport union, said: "There is already a massive skills shortage on rail infrastructure which is contributing to delays in delivering essential upgrade and renewal projects and that problem is set to grow over the coming years, compromising works crucial to keeping pace with surging passenger demand.
"The problem is worsened by fragmentation and casualisation in the rail industry which puts the critical issue of workforce planning as a very low priority against the demands to slash budgets and cut corners."
Dave Hulse, national officer of the GMB union, said: "We have been warning every employer connected to construction for a very long time that there was a need to recruit young apprentices into the industry.
"This report shows that these warnings were not heeded. The Government cannot afford to leave training for skills to chance.
"Higher nationally agreed rates of pay are needed to bring highly talented and skilled people back to the industry and encourage young people that there is a career in construction."
A Government spokesman said: "The Government is working closely with the housebuilding sector to ensure it has the skills it needs. This includes supporting construction firms to deliver courses from steel-fixing to digital engineering.
"Employers in different industries, including construction and rail, have been designing apprenticeship standards for the roles they need, as we deliver three million apprenticeships in the next five years."