Whilst it is recognised that targeting self-renewal is an effective way to functionally impair the quiescent leukaemic stem cells (LSC) that persist as residual disease in chronic myeloid leukaemia (CML), developing therapeutic strategies to achieve this have proved challenging. We demonstrate that the regulatory programmes of quiescent LSC in chronic phase CML are similar to that of embryonic stem cells, pointing to a role for wild type p53 in LSC self-renewal. In support of this, increasing p53 activity in primitive CML cells using an MDM2 inhibitor in combination with a tyrosine kinase inhibitor resulted in reduced CFC outputs and engraftment potential, followed by loss of multilineage priming potential and LSC exhaustion when combination treatment was discontinued. Our work provides evidence that targeting LSC self-renewal is exploitable in the clinic to irreversibly impair quiescent LSC function in CML residual disease – with the potential to enable more CML patients to discontinue therapy and remain in therapy-free remission.