Records of students' course marks are being proposed to replace England's 200-year-old degree classifications.
Prof Burgess said he wanted more information to be available
A steering group representing university chiefs and funding councils has come up with proposals for more information on students' achievements.
This would include simpler overall grades of Distinction, Pass and Fail.
The group was established amid concern there is too much emphasis on degree classifications, and with many degrees bunched at the 2:1 level.
Although centred on English institutions, the proposals have UK-wide implications.
The steering group report said honours degree classifications "may not be the best way of providing students with the detailed information they need about their performance, and of providing employers with the information they need to select employees".
It said they gave a "snapshot" not in keeping with the aim of lifelong learning.
It has suggested a greater emphasis on a "richer representation" of student achievement by means of a transcript.
This might include grades for coursework, unseen examinations, group work and project work at different levels of study.
It would incorporate a much-reduced overall scale of Distinction, Pass and Fail grades.
A separate report invites ideas on how credits for students' achievements might best be organised.
The group was chaired by Professor Robert Burgess, Vice-Chancellor of the University of Leicester.
In an earlier report he concluded that the existing system had "outlived its usefulness and is no longer fit for purpose".
He said on Thursday: "The current UK honours system is a robust, internationally recognised qualification, but we need to ensure that a greater wealth of information is available to employers, students and institutions themselves.
"We also need to consider ways in which there can be a more coherent approach to credit in England."
The president of Universities UK, the vice-chancellors' group, Professor Drummond Bone, said: "The aim of the consultation is to help institutions to better equip graduates with a fair reflection of the full activities and hard work that they've put in whilst studying at university - and to facilitate greater mobility for students at any point in their studies.
"Our members have clearly indicated the need to consider the current degree classification system and the consultation paper offers them that opportunity."
People's opinions on the proposals are being sought by 18 November.