Headteachers urged vice-chancellors this week not to "bypass" plans to reform the exam system for 14 to 19-year-olds by setting up their own admissions tests to select candidates.
The National Association of Headteachers has warned that the proposed new diploma to replace GCSEs and A levels could be undermined if universities introduced their own entrance exams.
A number of higher education institutions already use entry tests, and others are considering them as a way to select the best candidates from the rising numbers applying with top grades.
The NAHT has told the working group on 14-19 reform - which is chaired by Mike Tomlinson, the former chief inspector of schools - that it would also be unacceptable for universities to admit students on the basis of their performance in some but not all units of the proposed diploma.
In its interim report published earlier this year, Mr Tomlinson's working party recommended that GCSEs and A levels be absorbed into a new diploma over ten years.
The new diploma would include specialist units in particular subjects and compulsory core units that would focus on literacy, numeracy and information technology skills.
The core skills element would help to address the problem of students entering university without the required basic communication and maths skills, Mr Tomlinson has said.
His working group has also suggested introducing more differentiation at the "top end" of the grading system and giving universities a detailed transcript of a student's performance to help them to distinguish between the brightest candidates. Pupils studying at the advanced level of the diploma would be expected to undertake a "dissertation-like" project to test their independent learning and research skills.
The NAHT said: "We are concerned at the current moves towards universities or groups of universities setting their own admissions tests.
"We are firmly of the view that the assessment arrangements, together with the grading and transcripts of achievement recorded in the proposed diploma system, should ensure differentiation between applicants and identify high-fliers."
In its formal response to the Tomlinson working group, Cambridge University welcomed more differentiation between high-achieving students and urged the group to develop proposals to "stretch and challenge' the country's most able students.
However, the university added: "There is strong evidence that many of the problems that this report seeks to address have their roots in the first two years of secondary education, which for many young learners seem to be little more than an exercise in treading water."
The Tomlinson group's final recommendations will be published this year.