This is a multi-centre, non-randomised, open label Phase I clinical trial of an Advanced Therapy Investigational Medicinal Product (ATIMP) in adults (age 16 to 65 years) with high risk, relapsed/refractory CD19+ B-ALL. The ATIMP for this study is cryopreserved autologous patient-derived T-cells transduced with a lentiviral vector to generate the CD19CAT-41BBZ CAR T-cells (referred to subsequently as CD19CAR T-cells). Patients will undergo an unstimulated leucapheresis for the generation of the ATIMP which will take approximately 15 days to generate. During this period, patients may receive "holding" chemotherapy as per institutional practice to maintain disease control. Patients will receive pre-conditioning lymphodepleting chemotherapy with cyclophosphamide 60mg/kg on Day -6 and fludarabine 30mg/m2 administered over 3 days (Day -5 to Day -3).