Clonal populations of mammalian cells are inherently heterogeneous. They contain cells that display non-genetic variability resulting from gene expression noise and the fact that gene networks have multiple stable states. These stable, heritable variants within one cell type can exhibit different levels of responsiveness to environmental conditions. Hence, they could in principle serve as a temporary substrate for natural selection in the absence of mutations. We suggest that such ubiquitous but non-genetic variability can contribute to the somatic evolution of cancer cells, hence accelerating tumour progression independently of genetic mutations.