Malignant rhabdoid tumour (MRT) is an often lethal childhood cancer that, like many paediatric tumours, is thought to arise from aberrant fetal development. The embryonic root and differentiation pathways underpinning MRT are not firmly established. Here, we study the origin of MRT by combining phylogenetic analyses and single-cell mRNA studies in patient-derived organoids. Comparison of somatic mutations shared between cancer and surrounding normal tissues places MRT in a lineage with neural crest-derived Schwann cells. Single-cell mRNA readouts of MRT differentiation, which we examine by reverting the genetic driver mutation underpinning MRT, SMARCB1 loss, suggest that cells are blocked en route to differentiating into mesenchyme. Quantitative transcriptional predictions indicate that combined HDAC and mTOR inhibition mimic MRT differentiation, which we confirm experimentally. Our study defines the developmental block of MRT and reveals potential differentiation therapies.