It showed a record 11 applications are being made for each apprenticeship vacancy in the UK.
The highest demand for apprenticeship schemes was in the business and administration sector, with 101,510 applications made.
Plumbing and heating was the most competitive field, with an average of 41 applicants for every vacancy. Animal care was also tough to break into, with more than 26 applicants for every apprenticeship.
This month's ONS figures revealed the number of 16-24 years olds out of work is approaching one million, so the pressure is growing on apprenticeship schemes.
Matthew Hancock, skills minister, said: "With more vacancies than ever before, apprenticeships are fast becoming the norm for young people who want to achieve their career goals through an alternative route to University.
"We want more employers to take advantage of the advice and support available from the NAS and consider how hiring an apprentice could benefit their business."
David Way, executive director of the NAS, said: "These figures show that the popularity of apprenticeships continues to rise and in a greater range of occupations than before. The increase in vacancies shows that more and more individuals are seeing apprenticeships as a great way to start out in their chosen career.
"Employers increasingly recognise that hiring apprentices is a great way of attracting new talent and developing a motivated, skilled and diverse workforce."
Earlier this year Government announced it would offer SMEs grants of £1,500 to take on 16-24-year-olds as an apprentice.
Jason Holt, entrepreneur and author of the Holt Review, said: "It is vital we do more to demonstrate how all employers can grow their own workforce through apprenticeships.
"For smaller businesses, this is even more crucial as apprentices help improve productivity while reducing costs."
