The apprenticeship task force says the scheme will not meet employers'
demands unless it is available beyond the present level 3 (A-level equivalent).
The task force was set up by government to give industry a say in the content of apprenticeships and promote the scheme among employers.
It says the Department for Education and Skills should "remove the obstacles" that prevent apprenticeships being offered at level 4 and beyond. Its interim report says: "Level 4 apprenticeships also offer the potential to address public-sector skills shortages in traditional graduate occupations."
The DfES is already working with Semta, the engineering sector skills council, on a "foundation degree apprenticeship", but the task force believes the idea could be introduced more widely. It said progression beyond level 3 could address the shortage of graduate recruits in local government.
In private industry, there is evidence that apprentices could progress to management if the scheme were extended.
At defence firm BAE Systems and supermarket chain Tesco, the apprenticeship programme is considered to offer 70 per cent of the skills required for management roles. At BT Retail, part of British Telecom, a quarter of senior managers started at apprenticeship level.
Apprenticeships are promoted by the Confederation of British Industry and backed by the Trades Union Congress.
The task force says the Learning and Skills Council must improve marketing of the scheme in industries which have "relatively low take-up" alongside colleges and providers that run the courses, even though the LSC has boosted participation to a record level of 250,000 people.
But there are problems with completion rates, the reports says, and drop-out rates are especially high in hospitality, with less than a quarter of apprentices reaching the end of the course.
The task force said it also wanted more women in traditionally male jobs, and pointed out that just 5 per cent of engineering apprentices are female.