Understanding the cellular mechanisms of tumour growth is key for designing rational anticancer treatment. Here we used genetic lineage tracing to quantify cell behaviour during neoplastic transformation in a model of oesophageal carcinogenesis. We found that cell behaviour was convergent across premalignant tumours, which contained a single proliferating cell population. The rate of cell division was not significantly different in the lesions and the surrounding epithelium. However, dividing tumour cells had a uniform, small bias in cell fate so that, on average, slightly more dividing than non-dividing daughter cells were generated at each round of cell division. In invasive cancers induced by Kras(G12D) expression, dividing cell fate became more strongly biased towards producing dividing over non-dividing cells in a subset of clones. These observations argue that agents that restore the balance of cell fate may prove effective in checking tumour growth, whereas those targeting cycling cells may show little selectivity.