Employers are running out of options to fill vacancies, with sectors like the NHS worst affected, says a report.
Demand for staff was the strongest in almost two years, but the number of candidates had plummeted, said the Recruitment and Employment Confederation (REC).
Demand for permanent staff increased across all categories in May, especially in engineering and nursing, said the report.
The slowest increase in demand was for construction workers.
Nursing, medical and care employees were the most in-demand type of short-term staff in May.
Tom Hadley, REC's director of policy, said the challenges facing the next government were stark, adding: "Official data shows unemployment has dropped to the lowest level since 1975, and EU citizens are leaving the UK in droves.
"Employers seeking to fill vacancies are running out of options.
"Skill shortages are causing headaches in many sectors.
"The NHS, for example, is becoming increasingly reliant on short-term cover to fill gaps in hospital rotas because there aren't enough nurses to take permanent roles.
"Meanwhile, the shortage of people with cyber security skills is a particular concern in many businesses.
"Whichever party forms the next government must focus on improving the employability of our young people and boosting inclusion for under-represented groups.
"Alongside this, these figures clearly show that in many sectors we need more, not fewer, people so that businesses can grow and public services continue to deliver."