Tumour progression involves a series of phenotypic changes to cancer cells, each of which presents therapeutic targets. Here, using techniques adapted from microbial experimental evolution, we investigate the evolution of tumour spreading - a precursor for metastasis and tissue invasion - in environments with varied resource supply. Evolutionary theory predicts that competition for resources within a population will select for individuals to move away from a natal site (i.e. disperse), facilitating the colonisation of unexploited resources and decreasing competition between kin. After approximately 100 generations in environments with low resource supply, we find that MCF7 breast cancer spheroids (small in vitro tumours) show increased spreading. Conversely, spreading slows compared to the ancestor where resource supply is high. Common garden experiments confirm that the evolutionary responses differ between selection lines; with lines evolved under low resource supply showing a plastic spreading phenotype. These differences in spreading behaviour between selection lines are heritable (stable across multiple generations), and show that the divergently evolved lines differ in their response to resource supply. It is possible that prolonged resource limitation itself causes a stable switch toward dispersal-like behaviour and an increased sensitivity to resource availability without the need for genetic change. Different clinical strategies may be needed depending on whether tumour progression is due to stable or plastic effects. This study highlights the effectiveness of experimental evolution approaches in cancer cell populations and demonstrates how simple model systems might enable us to observe and measure key selective drivers of clinically important traits.