Quinn was especially involved in
ecumenical matters. In the
Secretariat for Promoting Christian Unity, he was observer at the General Assembly of the
World Alliance of Reformed Churches at
Frankfurt in 1964, was consultor to the Secretariat 1968–1973, and was consultant at the
World Council of Churches Faith and Order meeting at
Leuven,
Belgium, in 1972 and at the fourth session of the SPCU/WARC dialogues at
Zeist, the
Netherlands, in 1973. In the
British Council of Churches he participated in its Faith and Order Conference in 1964 and in its Church Leaders' Conference in 1972; and, on behalf of the
Scottish Catholic Hierarchy, was consultant/observer from 1966 and consultant to the board of its division of Ecumenical Affairs from 1975. In the Commission for Christian Unity (formerly the National Ecumenical Commission of Scotland) he was secretary of the Joint Study Group (with the
Scottish Episcopal Church) from 1968 to 1976, and was a member of the Joint Commission on Christian Marriage, and of the Dialogue on the Mutual Recognition of Baptism (both with the
Church of Scotland). In 1987
Cardinal Keith O'Brien appointed him
Episcopal Vicar for
Ecumenism in the
Archdiocese of Edinburgh. ==Consultancy and writing==