Inclusion Criteria:  1. Histologically confirmed cancer of the urinary tract with squamous cell carcinoma histology and without any TCC component. Mixed non-TCC histology is allowed if squamous cell carcinoma is the predominant histology 2. Newly diagnosed or progressive measurable disease as defined by RECIST version 1.1. To be considered measurable (and to be designated as a target lesion), a lesion must not have been treated with prior radiotherapy or focal ablation techniques 3. Suitable, in the judgment of the local investigator, for treatment with atezolizumab, with palliative intent 4. Adequate haematologic and end-organ function within 28 days prior to the first study treatment including:  Absolute neutrophil count ≥ 1.5 x109/L Platelet count ≥ 100 x109/L Haemoglobin ≥ 90 g/L Aspartate transaminase (AST), alanine transaminase (ALT), and alkaline phosphatase ≤ 2.5 times the institutional upper limit of normal (ULN) Total bilirubin ≤ 1.5 times ULN (or ≤ 3 ULN in patients with Gilbert's syndrome) Calculated creatinine clearance ≥ 20 mL/min (Cockcroft-Gault formula) 5. Up to one prior line of systemic chemotherapy for UTSCC 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 7. Life expectancy ≥ 12 weeks 8. Representative formalin-fixed paraffin-embedded (FFPE) tumour sample with an associated linked-anonymised pathology report that is available for central use in translational studies 9. Able to comply with all trial procedures and processes 10. Aged 18 years or over 11. Provision of written informed consent  Exclusion Criteria:  Any component of TCC histology Planned for treatment with curative intent Prior systemic immunotherapy (prior intra-vesical treatments are allowed) Major surgery within 30 days prior to enrolment History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins Known hypersensitivity to biopharmaceuticals produced in Chinese hamster ovary cells or any component of the atezolizumab formulation Use of oral or IV steroids for 14 days prior to enrolment. Use of inhaled corticosteroids, physiologic replacement doses of glucocorticoids (i.e., for adrenal insufficiency), and mineralocorticoids (e.g., fludrocortisone) is allowed Administration of a live or attenuated vaccine within 4 weeks prior to enrolment (COVID-19 vaccination is allowed) Treatment with any other investigational agent within 4 weeks prior to enrolment Coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, unstable arrhythmias, unstable angina or congestive cardiac failure (New York Heart Association ≥ grade 2) within 6 months prior to enrolment Patients with known HIV infection or with active tuberculosis Patients with known active hepatitis B virus (HBV; chronic or acute; defined as having a positive hepatitis B surface antigen [HBsAg] test) or hepatitis C. Patients with past HBV infection or resolved HBV infection (defined as the presence of hepatitis B core antibody and the absence of HBsAg) are eligible. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA Autoimmune disease including myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. Patients with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone or with controlled Type I diabetes mellitus on a stable dose of an insulin regimen are eligible for this study History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan. A history of radiation pneumonitis in the radiation field (fibrosis) is permitted Prior allogeneic stem cell or solid organ transplant Patients who are pregnant or breastfeeding Patients of child-bearing potential who are not able to use a highly effective method of contraception (as detailed in section 3.6) A recent or current other cancer. Current non-melanoma skin cancer, cervical carcinoma in situ, or localized prostate cancer not requiring current treatment are permissible, as is a history of a separate other malignancy having completed all active treatment ≥2 years previously