* Involvement in the planning and/or conduct of the study.
* Concurrent enrolment in another clinical study, unless it is an observational (non-intervention) clinical study or the follow-up period of an interventional study.
* Receipt of any conventional or investigational anticancer therapy within 4 weeks prior to the planned first dose of olaparib and durvalumab.
* Any previous treatment with PARP inhibitor or PD-1/PD-L1 inhibitors including olaparib and durvalumab.
* Other malignancy within the last 5 years with exceptions.
* Resting ECG with QTc > 470 msec or family history of long QT syndrome.
* Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 4 weeks prior to planned start of study treatment.
* Concomitant use of known strong or moderate CYP3A inducers. The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. This criterion does not apply to patients in Cohort A.
* Persistent toxicities caused by previous cancer therapy, excluding alopecia and laboratory values listed per the inclusion criteria.
* Patients with myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML.
* Patients with symptomatic uncontrolled brain metastases.
* Major surgery within 2 weeks of starting study treatment. Patients must have recovered from any effects of any major surgery to be considered eligible.
* Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection.
* Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of olaparib.
* Female patients who are pregnant, lactating, or intend to become pregnant during their participation in this study.
* Immunocompromised patients.
* Patients with a known hypersensitivity to olaparib or durvalumab or any of the excipients of the products.
* Patients with known active hepatitis (i.e. Hepatitis B or C).
* Patients requiring whole blood transfusions in the last 120 days prior to entry to the study.
* Current or prior use of immunosuppressive medications within 14 days before the 1st dose with exceptions.
* Active or prior documented autoimmune or inflammatory disorders within the last 2 years.
* History of allogenic organ transplantation.
* Any condition that, in the opinion of the investigator, would interfere with evaluation of the investigational products or interpretation of patient safety or study results.
* Prior enrolment in this study.
* Receipt of liver attenuated vaccines within 30 days prior to the 1st dose of investigational products, during the study and 30 days after the last dose of study treatments.
* Known active infection including tuberculosis.