More than 1.4 million applications were made for vacancies in the past 12 months.
Demand far outstripped supply, with an average of 11 applicants for each of the 129,000 vacancies posted online.
The NAS said apprenticeships continue to appeal to employers, with close to 129,000 vacancies posted online in 2012/13 compared with 101,000 in 2011/12.
Skills minister Matthew Hancock said he wanted to see it become the norm that young people either go to university or into an apprenticeship.
"To match the growing popularity of apprenticeships, I would urge more employers to consider how hiring an apprentice could benefit their business," he said.
Live event promotion was the most popular job area, with 35 applicants per vacancy. Vacancies in plumbing were the next most popular, with 33 applicants for each apprenticeship.
London had the most competition for places, with potential apprentices submitting almost 285,000 applications.
