Recent advances in molecular profiling provide descriptive datasets of complex differentiation landscapes including the haematopoietic system, but the molecular mechanisms defining progenitor states and lineage choice remain ill‐defined. Here, we employed a cellular model of murine multipotent haematopoietic progenitors (Hoxb8‐FL) to knock out 39 transcription factors (TFs) followed by RNA‐Seq analysis, to functionally define a regulatory network of 16,992 regulator/target gene links. Focussed analysis of the subnetworks regulated by the B‐lymphoid TF Ebf1 and T‐lymphoid TF Gata3 revealed a surprising role in common activation of an early myeloid programme. Moreover, Gata3‐mediated repression of Pax5 emerges as a mechanism to prevent precocious B‐lymphoid differentiation, while Hox‐mediated activation of Meis1 suppresses myeloid differentiation. To aid interpretation of large transcriptomics datasets, we also report a new method that visualises likely transitions that a progenitor will undergo following regulatory network perturbations. Taken together, this study reveals how molecular network wiring helps to establish a multipotent progenitor state, with experimental approaches and analysis tools applicable to dissecting a broad range of both normal and perturbed cellular differentiation landscapes.