Blackburn was born in Huddersfield in 1939 to Wilfred, a painter and decorator, and Nora. As an only child, Blackburn spent his time painting and walking on the moors near his home; it is this period which he credits as helping him to the cultivate the ‘strong inner vision’  which is a major hallmark of his art. After securing a scholarship to the local grammar school, Blackburn studied at the Huddersfield School of Art for several years. His friends included the playwright David Halliwell, whose play Little Malcolm and his Struggle Against the Eunuchs was loosely based on the students who attended the college, and the children's television personality Wilf Lunn.
On the advice of his tutor, Blackburn successfully applied for a place at the Royal College of Art, where he studied from 1959–1962. Although he was initially based in the Textile Department, students were encouraged to move between areas, and Blackburn quickly found himself drawn to the more subtle challenges of landscape art, a slightly unfashionable subject at the time. Many of Blackburn's contemporaries, including David Hockney and R.B. Kitaj, were gaining major critical recognition for their innovations in what would soon become known as Pop Art, or 'Royal College Pop'. Blackburn was unmoved by the playful aesthetic of such trends, preferring instead the quieter visions of landscape artists such as Gerhart Frankl and Prunella Clough, the former of whom went on to become a major influence and personal friend.