Complex sentence: The most successful and best known of the bands associated with the movement are Oasis, Blur, Suede and Pulp; those groups would come to be known as its "big four".
Split into simpler sentences: The most successful and best known of the bands associated with the term are Oasis, Blur, Pulp, and Suede. Over time, Oasis, Blur, Suede and Pulp emerged as the movement's "big four".