A three-dimensional chromatin state underpins the structural and functional basis of the genome by bringing regulatory elements and genes into close spatial proximity to ensure proper, cell-type specific gene expression profiles. However it is still unclear if the epigenome is involved in shaping the three-dimensional (3D) chromatin architecture and how this is altered in cancer. We performed Whole Genome Bisulphite Sequencing (WGBS), ChIP-seq, Hi-C chromosome conformation capture and replication timing sequencing to investigate how 3D chromatin organization in relation to the epigenome is disrupted in cancer. To our surprise we find a direct relationship between chromatin modifiying enzymes and the pattern of DNA methylation at CpG island promoters. In addition we reveal a conserved class of CTCF sites that are important in the maintenance of chromatin structure and gene expression. Moreover our study provides new insights into the relationship between replication timing, long-range epigenetic deregulation and changes in higher-order chromatin interactions in cancer.