1. Aged ≥18 years at Screening 2. Major depression without psychotic features (single or recurrent episode as informed by the Diagnostic and Statistical Manual of Mental Disorders, 5th edition [DSM-5]) 3. If the current major depressive episode is the participant's first lifetime episode of depression, the length of the current episode must be ≥3 months and ≤2 years at Screening 4. MADRS total score ≥20 at Screening and Baseline to ensure at least moderate severity of depression 5. TRD, defined as failure to respond to an adequate dose and duration of two, three, or four different pharmacological treatments for the current episode as determined through the Massachusetts General Hospital Antidepressant Treatment Response Questionnaire (MGH-ATRQ) and using the supplementary advice on additional antidepressants not included in MGH-ATRQ. 6. At Screening, agreement to discontinue all prohibited medications.

Psychiatric Exclusion Criteria: 1. Prior or ongoing bipolar disorder, any psychotic disorder, including schizophrenia, schizophreniform disorder, schizoaffective disorder, brief psychotic disorder (unless substance induced or due to a medical condition), antisocial personality disorder as assessed by a structured clinical interview (MINI 7.0.2) 2. Lifetime paranoid, schizoid, schizotypal, histrionic, narcissistic personality disorder, or any ongoing serious psychiatric comorbidity based on medical history and clinical judgement 3. Borderline personality disorder as demonstrated by medical history or the Mini International Neuropsychiatric Interview Plus (MINI plus) - borderline personality disorder module 4. Ongoing post-traumatic stress disorder, obsessive-compulsive disorder, or anorexia nervosa as assessed by medical history and a structured clinical interview (MINI 7.0.2) 5. Psychiatric inpatient within the past 12 months prior to Screening 6. Use of electroconvulsive therapy, deep brain stimulation, or vagus nerve stimulation during the current depressive episode 7. Transcranial magnetic stimulation within the past six months prior to Screening 8. Current enrolment in a psychological therapy programme that will not remain stable for the duration of the study. Psychological therapies cannot have been initiated within 30 days prior to Screening 9. Exposure to COMP360 psilocybin therapy prior to Screening