The call for the reforms comes from the National Advisory Council for Education and Training Targets, the Government body charged with raising the country's standards by the next century.
It effectively pre-empts the results of a review of 16-19 qualifications which was launched this week by Education Secretary Gillian Shephard at the annual conference of the Secondary Heads Association. Sir Ron Dearing, chairman of the School Curriculum and Assessment Authority, has been asked to recommend ways to increase participation in A-levels and vocational qualifications, raise standards and cut failure rates.
In a cautiously-worded brief to Sir Ron, Mrs Shephard stresses the need to "maintain the rigour of A-levels".
However, in her speech to SHA, she called for a hard look at basic skills. In her former role as Employment Secretary, she backed a call for core skills in A-levels from the Confederation of British Industry.
At the SHA conference she said: "Should we encourage core skills, which are already an essential part of General National Vocational Qualifications, as part of the programmes of study for more 16 to 19-year-olds? I believe we should."
Mrs Shephard said she saw room for core skills courses running beside A-levels. The advisory council's targets which she is understood to back go further, incorporating them into many courses.
The six core skills which ministers are set to endorse amount to much more than simple maths and English tests. They would include wider communication skills, practical use of maths, information technology, problem-solving techniques, the ability to work in teams and personal study skills. Some of these are already required for GNVQs. However, the advisory council wants the full range introduced for all 16 to 19-year-olds.
The inclusion of core skills is certain to provoke controversy with traditionalist Tories who have successfully fought moves to reform A-levels.
However, the council's recommendations are understood to have the backing of Employment Secretary Michael Portillo, Welsh Secretary John Redwood, both important right-wing allies, as well as Mrs Shephard. All three departments are also backing Sir Ron's post-16 review.
Ministers have come under ever-increasing pressure from industry over core skills. A-levels have been repeatedly criticised by industrialists for leaving students ill-prepared for work.
The CBI has been the most vociferous. In its submission to the council's latest review of national targets, the CBI suggests a target that "all academic and vocational qualifications be designed to deliver core skills by the year 2000".
The Employment Department, which is responsible for National Vocational Qualifications, this week welcomed the wider post-16 review by Sir Ron. If the review is to bring more coherence 16-19 then the full co-operation of both the employment and education departments is needed.
An employment spokesman gave a strong hint that they would like to see wider reforms so that people could "mix and match qualifications". He said: "We have no bias in favour of vocational against academic qualifications. Nor does the DFE have a bias in favour of the academic."
Education ministers have also given increasing hints of their willingness to see A-level reforms. Eric Forth, Minister of State, signalled a possible shake-up of post-16 education at the National Association of Head Teachers' conference last month. Insisting that he was "more broad minded" than teachers thought, Mr Forth said GNVQs had broken "the monopoly of A-levels".