How cell-to-cell copy number alterations that underpin genomic instability1 in human cancers drive genomic and phenotypic variation, and consequently the evolution of cancer2, remains understudied. Here, by applying scaled single-cell whole-genome sequencing3 to wild-type, TP53-deficient and TP53-deficient;BRCA1-deficient or TP53-deficient;BRCA2-deficient mammary epithelial cells (13,818 genomes), and to primary triple-negative breast cancer (TNBC) and high-grade serous ovarian cancer (HGSC) cells (22,057 genomes), we identify three distinct ‘foreground’ mutational patterns that are defined by cell-to-cell structural variation. Cell- and clone-specific high-level amplifications, parallel haplotype-specific copy number alterations and copy number segment length variation (serrate structural variations) had measurable phenotypic and evolutionary consequences. In TNBC and HGSC, clone-specific high-level amplifications in known oncogenes were highly prevalent in tumours bearing fold-back inversions, relative to tumours with homologous recombination deficiency, and were associated with increased clone-to-clone phenotypic variation. Parallel haplotype-specific alterations were also commonly observed, leading to phylogenetic evolutionary diversity and clone-specific mono-allelic expression. Serrate variants were increased in tumours with fold-back inversions and were highly correlated with increased genomic diversity of cellular populations. Together, our findings show that cell-to-cell structural variation contributes to the origins of phenotypic and evolutionary diversity in TNBC and HGSC, and provide insight into the genomic and mutational states of individual cancer cells.