Platinum and Polyadenosine 5'Diphosphoribose Polymerisation Inhibitor for Neoadjuvant Treatment of Triple Negative Breast Cancer and/or Germline BRCA Positive Breast Cancer

Inclusion Criteria: * Aged between 16 and 70. * Written informed consent, willing and able to comply with the Protocol for the duration of the trial including undergoing treatment and scheduled visits and examinations. * Histologically confirmed invasive breast cancer. * ER-negative\*, and HER2-negative\*\* breast cancer (TNBC). Patients will be eligible with any PR status but PR expression must be scored. OR * Germline BRCA (gBRCA) mutation positive, HER2 negative, and PgR / ER of any status. * T1, T2 or T3 tumours. * T4 tumour of any size with direct extension to (a) chest wall or (b) skin. OR Inflammatory carcinoma with tumour of any size. OR Other Locally Advanced Disease: * Involvement of ipsilateral large or fixed axillary lymph nodes, or infra or supraclavicular nodes (\>10mm diameter or clinical N2 or N3) and primary breast tumour of any diameter. * Involvement of ipsilateral large or fixed axillary lymph nodes, or infra or supraclavicular nodes (\>10mm diameter, or clinical N2 or N3), without a primary breast tumour identified, the presence of breast cancer in a Lymph Node (LN) must be histopathologically confirmed by LN biopsy. OR Multifocal tumour: \- with at least one tumour with a size\>10mm. * Patients with bilateral disease are eligible to enter the trial provided that both breast disease meets the above criteria. * Be fit to receive the trial chemotherapy regimen in the opinion of the responsible clinician: Adequate bone marrow, hepatic, and renal function. ECOG performance status of 0, or 1. * Treatment should be commenced within 6 weeks of the diagnostic biopsy. In uncommon circumstances, where medically acceptable, treatment is permitted to start within a maximum of 9 weeks of the diagnostic biopsy. * Availability of the Tumour Infiltrating Lymphocytes score is required. * Availability of CK 5/6 and EGFR +/- Androgen Receptor IHC score. * Availability of slides and paraffin embedded tissue blocks from pre-chemotherapy core biopsy and from primary surgical resection is required. * Women of child-bearing potential (WCBP), defined as not surgically sterilized or not post-menopausal for at least 24 consecutive months if age ≤55 year or 12 months if age \>55 years, must have a negative serum or urine pregnancy test within 14 days prior to randomisation. * All WCBP and all sexually active male patients as well as their partners must be aware that they should not conceive during the treatment period and therefore should routinely use effective forms of contraception, throughout their participation in the trial and for at least 6 months after the last dose of trial treatment. Please follow the olaparib contraception guidelines. Exclusion Criteria: * T0 tumour in absence of axillary node \>10mm. * TNBC with a non-basal phenotype which strongly expresses Androgen Receptor. * Previous or concomitant chemotherapy or biological agents used for the treatment of cancer in the last 5 years. * Malignancy within the last 5 years except: adequately treated non-melanoma skin cancer; curatively treated in situ cancer of the cervix; ductal carcinoma in situ (DCIS); Stage 1, grade 1 endometrial carcinoma; or other solid tumours including lymphomas (without bone marrow involvement) curatively treated with no evidence of disease for ≥5 years. * Patients with myelodysplastic syndrome/acute myeloid leukaemia. * Evidence of distant metastasis apparent prior to randomisation. * Patients with uncontrolled seizures. * Pre-existing sensory or motor neuropathy of CTCAE v4.03, grade ≥2. * Concomitant use of known potent CYP3A4 inhibitors and inducers. Consider wash-out periods. * Pregnant or breast feeding women. * Not suitable for neoadjuvant chemotherapy in the opinion of the responsible clinician. * Major surgery within 14 days of starting trial treatment and patients must have recovered from any effects of any major surgery. * Any evidence of other disease or any concomitant medical or psychiatric problems which in the opinion of the Investigator would prevent completion of treatment or follow-up. For example: Evidence of severe or uncontrolled cardiac disease Uncontrolled ventricular arrhythmia Recent myocardial infarction (within 12 months) Active infection including Hepatitis B, Hepatitis C and Human Immunodeficiency virus (HIV). Screening for chronic conditions is not required. * ECG with mean resting QTc \>470 msec on 2 or more time points within a 24 hour period or family history of long QT syndrome. * Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the trial medication * Known hypersensitivity to olaparib, carboplatin, paclitaxel or their excipients (including cremophor). * Whole blood transfusions in the last 120 days prior to blood sampling for BRCA test as it may interfere with the results (packed red blood cells and platelet transfusions are acceptable).