New starts fell by 19 per cent among 16- to 18-year-olds (from 131,400 to 106,600), and 26 per cent among 19- to 24-year-olds (from 153,900 to 113,700), between 2015/16 and 2017/18.
The bleak picture was echoed more widely, with levels across all ages down by 26 per cent, significantly down from pre-2017 reform levels, when the apprenticeship levy was introduced, according to the NAO report on the programme's value for money.
The government's target of creating three million apprenticeships by 2020 is therefore likely to be missed, unless the Department for Education does "much more to meet its ambitions", said NAO comptroller & auditor general Amyas Morse.
With many of the placements being aimed at vulnerable and disadvantaged young people - for whom apprenticeships are a vital route into employment - the fall is a major blow.
In its 2015 spending review, the government assumed that apprenticeship starts among 16- to 18-year-olds would stay at around 128,000 a year, while the number of starts for older age groups would rise, according to the report.
To meet its target, the DfE would have to double the rate of starters taking up the scheme before March 2020.
Overall, numbers dropped to 375,800 in 2017/18, from 509,400 in 2015/16 which the last full year before reforms.
Morse said: "Despite making changes to the apprenticeships programme, the department has not enticed employers to use available funds or encouraged enough potential recruits to start an apprenticeship.
"If the DfE is serious about boosting the country's productivity, it needs to set out clearly whether its efforts are on track to meet that aim."
The report also raises concerns about the long-term financial sustainability of the programme.
While the take-up of levy funds is below the level budgeted (in 2017/18, it spent £1.6bn, which was £0.4bn less than budgeted), the NAO reports that if demand picked up and employers continued their preference for higher-cost apprenticeships, the department "could overspend against its budget in future".
It also warned that some employers were replacing existing graduate training schemes with apprenticeships, meaning the amount the government was investing in the schemes would not result in marked additional value to the economy.
The report states: "There are risks that the programme is subsidising training that would have happened without government funding, and the department has not set out clearly how it measures the impact of the programme on productivity.
"Given these concerns, the department has some way to go before it can demonstrate that the programme is achieving value for money and that resources are being used to best effect."
The report also found that although the DfE was likely to meet two of its diversity targets, these did not reflect national representation of the groups.
The DfE aimed to have 25 per cent of apprentices from "the most disadvantaged areas", but it achieved a rate of only 22.6 per cent.
Apprenticeship and skills minister Anne Milton said: "Apprenticeships enable people to get a great job and career, and give employers the skilled workforce they need.
"We have increased flexibility for levy-paying employers so they can transfer 10 cent of their levy funds to other employers and we will increase this to 25 per cent from April."