The resulting qualification, which could be called a diploma or a pass degree, would mean for many the completion of their higher education, while for others it could be a stage on the road to an honours degree.
The proposal, which has echoes of the "associate degree" offered by junior colleges in the United States, would boost the country's education and training system at the level where it is weakest and help maintain the standard of the honours degree at a time of expansion.
"Over-proliferation of degrees may well endanger their value, be costly and risk the charge that higher education is becoming a trivial activity," warn the seven associations in their joint submission.
But the heads say the three-year degree should remain the basic building-block of higher education. For younger entrants, three years of full-time study should remain the norm. "Any shorter course is unlikely to provide the personal development required or to equip students with sufficient basic skill and knowledge," they argue. The degree course could be longer or shorter for older students, depending on their previous experience and education.
On student support, the secondary and college heads propose abolishing the present system of mandatory and discretionary grants and replacing it with a full loans scheme covering up to three years of maintenance and tuition fees. Students would repay the loan over an extended period, on terms related to their subsequent earnings.
The heads propose raising standards of teaching in higher education by introducing a teaching qualification for lecturers (a PGCHE), with a formal induction programme for new lecturers, regular appraisal and higher salaries for high performance.
The seven associations submitting their evidence jointly are: the Association of College Managers, the Association of Colleges, the Association of Principals in Sixth Form Colleges, the Girls' Schools Association, the Headmasters' and Headmistresses' Conference, the National Association of Head Teachers and the Secondary Heads Associations. The associations will also be submitting separate evidence.