The formation of red blood cells begins with the differentiation of multipotent haematopoietic progenitors. Reconstructing the steps of this differentiation represents a general challenge in stem-cell biology. Here we used single-cell transcriptomics, fate assays and a theory that allows the prediction of cell fates from population snapshots to demonstrate that mouse haematopoietic progenitors differentiate through a continuous, hierarchical structure into seven blood lineages. We uncovered coupling between the erythroid and the basophil or mast cell fates, a global haematopoietic response to erythroid stress and novel growth factor receptors that regulate erythropoiesis. We defined a flow cytometry sorting strategy to purify early stages of erythroid differentiation, completely isolating classically defined burst-forming and colony-forming progenitors. We also found that the cell cycle is progressively remodelled during erythroid development and during a sharp transcriptional switch that ends the colony-forming progenitor stage and activates terminal differentiation. Our work showcases the utility of linking transcriptomic data to predictive fate models, and provides insights into lineage development in vivo.