Haematopoietic stem and progenitor cells (HSPCs) have been the focus of developmental and regenerative studies, yet our understanding of the signalling events regulating their specification remains incomplete. We demonstrate that supt16h, a component of the Facilitates chromatin transcription (FACT) complex, is required for HSPC formation. Zebrafish supt16h mutants express reduced levels of Notch-signalling components, genes essential for HSPC development, due to abrogated transcription. Whereas global chromatin accessibility in supt16h mutants is not substantially altered, we observe a specific increase in p53 accessibility, causing an accumulation of p53. We further demonstrate that p53 influences expression of the Polycomb-group protein PHC1, which functions as a transcriptional repressor of Notch genes. Suppression of phc1 or its upstream regulator, p53, rescues the loss of both Notch and HSPC phenotypes in supt16h mutants. Our results highlight a relationship between supt16h, p53 and phc1 to specify HSPCs via modulation of Notch signalling.