Inclusion Criteria:

          -  Histologically confirmed acute myeloid leukaemia (AML) or acute lymphoblastic
             leukaemia (ALL) for which there are limited treatment options known to provide
             clinical benefit.

          -  Eastern cooperative oncology group performance status ≤2. Performance status must not
             have deteriorated by ≥2 levels within 2 weeks after providing informed consent.

          -  Predicted life expectancy ≥12 weeks.

          -  Adequate organ function at screening as per the protocol defined criteria.

          -  Adequate cardiac function as demonstrated by LVEF > 50% on screening cardiac
             multigated acquisition, magnetic resonance image or echocardiogram.

          -  Willing and able to participate in all required study evaluations and procedures
             including receiving IV administration of study treatment and admission to the
             hospital, when required, for administration of study treatment and monitoring.

          -  For inclusion in the genetic component of the study, participants must fulfil protocol
             defined criteria.

          -  White blood cell count must be <10 x 10^9/L. Treatment with hydroxyurea during
             screening and Cycle 1 to achieve this level is permitted.

          -  Women of childbearing potential and men should use protocol defined contraceptive
             measures.

        Exclusion Criteria:

          -  Unresolved toxicity from prior anticancer therapy of Common Terminology Criteria for
             Adverse Events Grade ≥2. Participants with Grade 2 neuropathy or Grade 2 alopecia are
             eligible.

          -  Active idiopathic thrombocytopenic purpura.

          -  Stem cell transplant < 6 months prior to the first dose of study treatment.

          -  Active graft versus host disease.

          -  Active central nervous system (CNS) leukaemia/leptomeningeal disease/spinal cord
             compression. Participants who have a history of CNS leukaemia must be free of CNS
             leukaemia for >30 days prior to the first dose of study treatment, and the most recent
             2 lumbar punctures must be negative for leukaemic cells, to be eligible.

          -  Active cytomegalovirus (CMV) infection (positive CMV Immunoglobulin M (IgM) and/or
             positive polymerase chain reaction (PCR) result).

          -  Active infection including human immunodeficiency virus, Hepatitis B, Hepatitis C, or
             severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2).

          -  As judged by the Investigator: any evidence of severe or uncontrolled systemic
             diseases, (eg, severe hepatic impairment, interstitial lung disease [bilateral,
             diffuse, parenchymal lung disease]); current unstable or uncompensated respiratory or
             cardiac conditions; Uncontrolled hypertension; history of, or active, bleeding
             diatheses (eg, haemophilia or von Willebrand disease); uncontrolled active systemic
             fungal, bacterial, or other infection.

          -  Any of the given cardiac criteria: history of cardiomyopathy, myocarditis or heart
             failure; mean resting corrected QT interval (QTcF) ≥470 msec obtained from 3
             electrocardiogram (ECGs), in the absence of a cardiac pacemaker; any clinically
             important abnormalities in rhythm, conduction or morphology of resting ECG; any
             factors that increase the risk of QTc prolongation or risk of arrhythmic events such
             as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT
             syndrome, or unexplained sudden death under 40 years of age.

          -  History of another life-threatening malignancy ≤2 years prior to first dose of study
             treatment with the exception of: malignancy treated with curative intent and with no
             evidence of active disease present for more than 2 years before screening and
             considered to be at low risk of recurrence by the treating physician; adequately
             treated lentigo malignant melanoma without current evidence of disease or adequately
             controlled non-melanomatous skin cancer; adequately treated carcinoma in situ without
             current evidence of disease.

          -  Any of the mentioned procedures or conditions currently or in the 6 months prior to
             the first dose of study treatment: coronary artery bypass graft; angioplasty; vascular
             stent; myocardial infarction; angina pectoris; congestive heart failure (New York
             Heart Association Class ≥2); ventricular arrhythmias requiring continuous therapy;
             ventricular arrhythmias requiring continuous therapy; haemorrhagic or thrombotic
             stroke, including transient ischaemic attacks or any other CNS bleeding.

          -  Treatment with any of the mentioned therapy: radiotherapy less than 3 weeks prior to
             first study treatment; immunotherapy or chemotherapy within ≤21 days or 5 half-lives
             prior to the first dose of study treatment. Treatment with one dose of cytarabine,
             steroids, or 6-mercaptopurine is permitted prior to the first dose of study treatment
             but these should be discontinued at least 2 days prior to the first dose of study
             treatment. Treatment with hydroxyurea is permitted as previously outlined;
             investigational drugs within ≤14 days or 5 half-lives (whichever is shorter) prior to
             the first dose of study treatment; major surgery (excluding placement of vascular
             access) ≤21 days, or minor surgical procedures ≤7 days, prior to the first dose of
             study treatment. No waiting is required mentioned implantable port or catheter
             placement; prescription or non-prescription drugs or other products known to be
             sensitive substrates of BCRP, OCT2, OAT3, OATP1B1, OATP1B3, CYP2B6, CYP2C8, CYP2C9 or
             CYP2D6, or reversible moderate or strong CYP3A inhibitors, which cannot be
             discontinued within 5 half-lives of the first dose of study treatment and withheld
             throughout the study until 14 days after the last dose of AZD0466; moderate or strong
             mechanism-based inhibitors or inducers of CYP3A4 which cannot be discontinued within 5
             half-lives plus 12 days of the drug prior to the first dose of study treatment and
             withheld until 14 days after the last dose of AZD0466; concurrent anti-coagulation
             therapy, including aspirin, which cannot be stopped; medications with known risk of
             Torsades de Pointes within 5 half-lives of the first dose of study treatment and
             continuing until 5 half-lives after the last dose of AZD0466; IV anti infection
             treatment within 14 days before first dose of study treatment.

          -  History of hypersensitivity to polyethylene glycol (PEG), PEGylated products or drugs
             with a similar chemical structure or class to AZD0466 or other BH3 mimetic.