Does Cediranib With Paclitaxel, or Cediranib and Olaparib, Treat Advanced Endometrial Cancer Better Than Paclitaxel?

Inclusion Criteria: 1. Histologically confirmed advanced or recurrent endometrial carcinoma or carcinosarcoma. 2. Aged \>16 years. 3. All participants must have received at least one prior line of platinum-based chemotherapy (either in the adjuvant or recurrent disease setting). In addition, ONE of the following must apply: 1. have disease recurrence/ progression within 18 months of completing adjuvant chemotherapy and have received no cytotoxic chemotherapy for recurrent/ progressive endometrial cancer. OR 2. have received one or two prior lines of cytotoxic chemotherapy for recurrent/ progressive endometrial cancer (not counting adjuvant treatment). 4. Dose-dense weekly paclitaxel is an appropriate treatment option. 5. Ability to provide written informed consent that includes genetic research on tissue derived from biopsies and biomarker research. (If a participant declines to participate in optional exploratory genetic research or the optional biomarker research, there will be no penalty or loss of benefit to the participant. The participant will not be excluded from other aspects of the study). 6. Willing and able to comply with the trial visits and undergo treatment as scheduled. 7. ECOG Performance Status 0-1. 8. Life expectancy greater than 16 weeks. 9. Measurable disease by RECIST v1.1 including at least one not previously irradiated lesion that is ≥ 10 mm in the longest diameter (lymph nodes must have short axis ≥ 15 mm) as determined by CT. 10. Adequate haematological function: Hb ≥ 90.0 g/l with no requirement for blood transfusion in the last 28 days, neutrophils ≥ 1.5 x 109/l, platelets ≥ 100 x 109/l; coagulation: INR \<1.4 (unless therapeutically anti-coagulated) and APPT ratio \<1.4. 11. Adequate liver function: bilirubin ≤1.5 x ULN, transaminases ALT and AST ≤2.5x ULN. (AST or ALT \<5x ULN allowed in the presence of parenchymal liver metastases. 12. Adequate renal function defined as calculated creatinine clearance using modified Wright or Cockcroft-Gault formula ≥ 51 ml/min or measured radioisotopic GFR ≥ 51ml/min. 13. Negative or trace proteinuria reading on urine dipstick. Patients with 1+ proteinuria on dipstick must have ≤1+ proteinuria on consecutive dipstick taken no less than 1 week later. Patients with ≥2+ proteinuria on dipstick must have 24 hour urinary protein excretion ≤1 g. 14. Adequately controlled thyroid function, with no symptoms of thyroid dysfunction. 15. Ability to swallow oral medication (tablets). 16. Willing to stop taking herbal supplements, and (if allocated to Arm 3) willing to not consume grapefruit or grapefruit juice, during the treatment period and for 30 days after end of trial treatment. Exclusion criteria 1. Prior treatment with dose-dense weekly paclitaxel. 2. Uncontrolled brain metastases or seizures. A scan to confirm the absence of brain metastases is not required. 3. Known positivity for hepatitis B, hepatitis C or HIV due to the risk of transmitting the infection through blood or other body fluids and potential for reactivation during treatment. 4. Resting ECG with QTc \> 470 ms on 2 or more time points within a 24 hour period or family history of long QT syndrome. 5. Concomitant use of known strong CYP3A inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting olaparib is two weeks. 6. Concomitant use of known strong CYP3A inducers (eg.phenobarbital,enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. 7. Pregnant or lactating. Pregnancy status in women of child bearing potential will be confirmed via a serum or urine pregnancy test prior to randomisation, monthly during the treatment period, and at the end of treatment assessment. 8. Of child bearing potential AND not willing to ensure they use effective contraception throughout the treatment period and for six months following the end of treatment. Acceptable methods of contraception are: i. true sexual abstinence (when this is in line with the preferred and usual lifestyle of the participant) ii. a combination of male condom plus one of: * vasectomised sexual partner, with participant assurance that partner received post-vasectomy confirmation of azoospermia * Tubal occlusion * Intrauterine device provided coils are copper-banded * Etonogestrel implants (eg, Implanon®, Norplant®) * Normal and low dose combined oral pills * Hormonal shot or injection (eg, Depo-Provera) * Intrauterine system device (eg, levonorgestrel-releasing intrauterine system -Mirena®) * Norelgestromin/ethinyl estradiol transdermal system * Intravaginal device (eg, ethinyl estradiol and etonogestrel) * Cerazette (desogestrel). Cerazette is currently the only highly efficacious progesterone based pill. 9. Side effects of previous treatments have not resolved to grade 1 or less, with the exception of alopecia that is considered related to cytotoxic chemotherapy. 10. Radiotherapy, chemotherapy, surgery or tumour embolisation within 28 days before the first dose of IMP. 11. Additional concurrent anti-cancer therapy. 12. Causes of malabsorption, e.g. uncontrolled diarrhoea or poorly controlled stoma. 13. Bowel obstruction, fistulae, impending fistulation seen on radiological imaging, or extensive rectosigmoid involvement by cancer. 14. Inadequately controlled hypertension, defined as ≥150/90 mmHg. 15. Prior or concurrent therapy with a PARP or VEGF inhibitor. 16. Known hypersensitivity to olaparib, cediranib or any of the excipients of the products. 17. Known hypersensitivity to paclitaxel that in the opinion of the investigator would prevent administration of a weekly paclitaxel regimen. 18. Exposure to an investigational agent within 30 days or 5 half-lives (whichever is the longer) prior to enrolment. 19. Considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. 20. Myelodysplastic syndrome (MDS), acute myeloid leukaemia (AML) or features suggestive of MDS/AML. 21. Other 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), or other solid tumours including lymphomas (without bone marrow involvement) curatively treated with no evidence of disease for ≥5 years. 22. Prior allogeneic bone marrow transplant or double umbilical cord blood transplantation.