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The research found growth of nearly 60% in businesses is held back by a skills gap in the wider workforce and among existing employees.
Miles Templeman, director-general of the IoD, said: "It is disturbing that, at a time of economic weakness, the growth of the private sector is being held back by skills shortages."
According to the survey, 31% of employers struggle to fill vacancies in their workforce, due to a shortage of applicants with the required skills.
Of the 1,100 directors surveyed, 47% said some of their organisation's employees lacked the skills to do their job to the required level.