It also rejects the growing push for managers with non-teaching backgrounds to be appointed to headship roles.
On teachers' pay, the group proposes giving state school heads similar freedoms to their colleagues in the fee-paying sector by creating a "nationally agreed minimum salary with appropriate annual increases continuing to be the benchmark, with schools freed to exceed the minimum". This represents a loosening of the current structure which stipulates teachers must be paid specific salary levels according to their career stage.
Any head wishing to vary these levels now without giving teachers extra responsibilities can pay additional amounts for recruitment and retention purposes. But the awards are for fixed periods and cannot be paid for more than three years.
The group, headed by Baroness Pauline Perry, a former chief inspector of schools, believes the increasing heads shortage will be "one of the greatest challenges facing any future Government".
It attributes much of the reluctance of teachers to become heads to the increasing administrative burden faced by school leaders.
But the group argues that the appointment of professional bursars in all larger schools, with shared arrangements for primaries, is a better solution than giving managers and administrators headships an idea proposed in an earlier Government-commissioned report.
"It is our firm belief the head should be a professional teacher, able to understand the issues which teachers face in the classroom, and to give professional leadership in curriculum and pedagogy."
The group proposes an absolute right for heads to exclude disruptive pupils and to use independent or voluntary alternatives to pupil referral units policies already backed by David Cameron, the Tory leader.
But the shadow cabinet is not expected to give immediate or automatic support to the rest of the group's report when it is released next week.