Inclusion Criteria:

          -  Morphologically proven relapsed/refractory (M2 or M3 marrow; ≥1st relapse for adults,
             ≥2nd relapse in paediatric group - see Protocol Appendix 5) or progressive B cell
             precursor or T-Acute Lymphoblastic Leukaemia (ALL) with demonstrated RAS pathway
             activating mutations (NRAS, KRAS, FLT3, PTPN11, cCBL) identified during the trial
             screening process

          -  Group P (paediatric): <18 years of age; Group A (adult): ≥18 years of age

          -  Adequate renal function:

               -  Group A: Serum creatinine <1.5 x upper limit of normal (ULN)

               -  Group P as follows:

                    -  5 years: Serum creatinine <0.8 mg/dL or 70 μmol/L, > 5 years but ≤ 10 years:
                       Serum creatinine <1 mg/dL or 88 μmol/L, > 10 years but ≤ 15 years: Serum
                       creatinine <1.2 mg/dL or 106 μmol/L, > 15 years: Serum creatinine <1.5 mg/dL
                       or 132 μmol/L

          -  Patient is able to swallow selumetinib capsules whole

          -  Performance status (PS): Group A - Eastern Cooperative Oncology Group (ECOG) ≤2
             (Protocol Appendix 6); Group P - Lansky play scale ≥60% (Protocol Appendix 7) or
             Karnofsky scale ≥60% (Appendix 8)

          -  Women of childbearing potential (see protocol section 7.9.3 for definition) must have
             a negative pregnancy test

          -  Patients who are women of childbearing potential and male patients with partners who
             are women of childbearing potential must agree to use appropriate contraception (see
             protocol section 7.9.3 for definition) whilst on trial

          -  Written informed consent

          -  Absence of any psychological, familial, sociological or geographical factors
             potentially hampering compliance with the trial protocol and follow-up schedule; those
             conditions should be discussed with the patient before registration in the trial

          -  Patients who relapse or progress after Haematopoetic Stem Cell Transplant (HSCT) need
             to be at least at day +100, with no signs of Graft versus Host Disease and off
             immunosuppressive therapy for at least one week.

          -  Patients who relapse or progress after CAR T cell therapy should be at least 4 weeks
             after infusion of CAR T cells.

          -  Patients must have a body surface area (BSA) ≥ 0.55 m2.

        Exclusion Criteria:

          -  ALL without presence of RAS-pathway activating mutations

          -  Mature B-cell leukaemia and Philadelphia positive ALL

          -  Prior exposure to MEK, RAS or RAF inhibitors

          -  Any unresolved toxicity ≥ CTCAE Grade 2 from previous anti-cancer therapy, except for
             alopecia

          -  Cardiac conditions as follows:

        Group A and P

          -  Prior or current cardiomyopathy including but not limited to the following:

               -  Known hypertrophic cardiomyopathy

               -  Known arrhythmogenic right ventricular cardiomyopathy

          -  Even if full recovery has occurred, previous moderate or severe impairment of left
             ventricular systolic function (LVEF <45% on Echocardiogram (ECHO) in Group A; SF <29%
             in Group P but excluding transient impairments due to e.g. anaemia/sepsis or results
             not thought to represent a true reflection of cardiac function)

          -  Severe valvular heart disease

          -  Severe congenital heart disease

          -  Uncontrolled hypertension:

               -  Group A: BP ≥150/95 mmHg despite medical therapy

               -  Group P: BP ≥95th percentile for age, height and gender (please refer to Blood
                  Pressure by Age and Height Percentiles tables in Protocol Appendices 8 and 9)
                  Group A

          -  Baseline (LVEF) below the lower limit of normal (LLN) or <55% measured by ECHO

          -  Acute coronary syndrome within 6 months prior to trial registration

          -  Uncontrolled Angina - Canadian Cardiovascular Society grade II-IV despite medical
             therapy (Protocol Appendix 11)

          -  Symptomatic heart failure New York Heart Association (NYHA) Class II-IV, prior or
             current cardiomyopathy, or severe valvular heart disease (Protocol Appendix 12)

          -  Atrial fibrillation with a ventricular rate >100 bpm on Electrocardiogram (ECG) at
             rest

          -  QTcF >450ms in male patients or ≥460ms in female patients, or other factors that
             increase the risk of QT prolongation Group P

          -  Baseline SF <29%

          -  Atrial fibrillation with a ventricular rate >130 bpm on Electrocardiogram (ECG) at
             rest

          -  QTcF >450ms in patients <12 years or ≥460ms in patients ≥12 but <18 years

          -  Ophthalmological conditions as follows:

               -  Current or past history of retinal pigment epithelial detachment (RPED)/central
                  serous retinopathy (CSR) or retinal vein occlusion

               -  Intraocular pressure (IOP) > 21 mmHg or uncontrolled glaucoma (irrespective of
                  IOP)

          -  Pregnant and breast feeding females

          -  Known severe hypersensitivity to selumetinib, dexamethasone or combination medications
             or any excipient of these medicinal products, or history of allergic reactions
             attributed to compounds of similar chemical or biologic composition to selumetinib

          -  Have received or are receiving an Investigational Medicinal Product (IMP) or other
             systemic anti-cancer treatment (not including dexamethasone, prednisolone or
             hydroxycarbamide) within 4 weeks (6 weeks for nitrosoureas, mitomycin, and suramin)
             prior to trial registration, or within a period during which the IMP or systemic
             anticancer treatment has not been cleared from the body (e.g. a period of 5
             'half-lives'), whichever is the most appropriate and as judged by the investigator

          -  Have had recent major surgery within a minimum 4 weeks prior to trial registration,
             with the exception of surgical placement of vascular access

          -  Have received radiation therapy within 4 weeks prior to trial registration, or limited
             field of radiation for palliation within 7 days of the first dose of trial treatment

          -  Laboratory values as listed below (SI units):

               -  Serum bilirubin >1.5 x ULN (unless due to Gilbert's syndrome)

          -  Have evidence of any other significant clinical disorder or laboratory finding that,
             as judged by the investigator, makes it undesirable for the patient to participate in
             the trial

          -  Have any evidence of a severe or uncontrolled systemic disease (e.g. unstable or
             uncompensated respiratory, cardiac, hepatic, or renal disease, active infection
             (including hepatitis B, hepatitis C, HIV), active bleeding diatheses, or renal
             transplant)

          -  Have refractory nausea and vomiting, chronic gastrointestinal diseases (e.g.,
             inflammatory bowel disease), or significant bowel resection that would adversely
             affect the absorption/bioavailability of the orally administered trial medication

          -  Any other active malignancy which, in the opinion of the investigator would limit the
             ability of the patient to complete the study