Madgwick was selected by the University of Sydney in December 1946 to fill the vacant post of Warden of New England University College in Armidale.
He assumed the office on 17 February 1947.

New England University College, established in 1938 under the University of Sydney, was still a small, fledgling institution.
At the time of Madgwick's appointment, the college had 202 full-time students, two faculties – arts and science – and no professors, only lecturers.
Most of the school's activities and facilities were contained in a single building- Booloominbah.
The New South Wales State Government Act, which created the college, stipulated that it would become independent as soon as it was considered ready.
The school, however, had made little progress towards official autonomy.
A formal request for funding and support to go independent submitted to the state by the school in September 1944 had gone unanswered.
In May 1945, the University of Sydney Senate mandated that the college be emancipated within seven years, but had thereafter taken no further action to ensure that its order was accomplished.
Among Madgwick's most pressing concerns upon assuming the office of warden was to resolve the question of independence for the school.

In response to the post–World War II baby boom, the New South Wales Department of Education, under Bob Heffron, queried the University of Sydney in 1951 on its thoughts about training and certifying schoolteachers by external studies and/or correspondence courses.
The university rejected the idea, stating that external degree or certification programs would be significantly inferior to residence education.
Undeterred, Heffron asked New England about its willingness to conduct external studies.
Madgwick enthusiastically supported the idea and instructed his college's staff to begin preparing an external studies program.
Heffron asked the University of Sydney if it had any objection to New England being granted independence to operate the state's external education program.
The university replied that it had no objection.

Heffron introduced the University of New England Act to the state parliament in early December 1953.
The governor signed the act into law on 16 December 1953 and the college became the independent University of New England on 1 February 1954.
Madgwick assumed the office of first Vice-Chancellor.
Madgwick was selected by the University of Sydney in December 1946 to fill the vacant post of Warden of New England University College in Armidale. He assumed the office on 17 February 1947.
New England University College, established in 1938 under the University of Sydney, was still a small, fledgling institution. At the time of Madgwick's appointment, the college had 202 full-time students, two faculties – arts and science – and no professors, only lecturers. Most of the school's activities and facilities were contained in a single building- Booloominbah. The New South Wales State Government Act, which created the college, stipulated that it would become independent as soon as it was considered ready. The school, however, had made little progress towards official autonomy. A formal request for funding and support to go independent submitted to the state by the school in September 1944 had gone unanswered. In May 1945, the University of Sydney Senate mandated that the college be emancipated within seven years, but had thereafter taken no further action to ensure that its order was accomplished. Among Madgwick's most pressing concerns upon assuming the office of warden was to resolve the question of independence for the school.
In response to the post–World War II baby boom, the New South Wales Department of Education, under Bob Heffron, queried the University of Sydney in 1951 on its thoughts about training and certifying schoolteachers by external studies and/or correspondence courses. The university rejected the idea, stating that external degree or certification programs would be significantly inferior to residence education. Undeterred, Heffron asked New England about its willingness to conduct external studies. Madgwick enthusiastically supported the idea and instructed his college's staff to begin preparing an external studies program. Heffron asked the University of Sydney if it had any objection to New England being granted independence to operate the state's external education program. The university replied that it had no objection.
Heffron introduced the University of New England Act to the state parliament in early December 1953. The governor signed the act into law on 16 December 1953 and the college became the independent University of New England on 1 February 1954. Madgwick assumed the office of first Vice-Chancellor.
Robert Madgwick