A Trial of ChAdOx1 and MVA Vaccines Against MAGE-A3 and NY-ESO-1

Patients with non-small cell lung cancer (NSCLC) or squamous oesophageal cancer will be entered into the trial as these tumour types are commonly known to have MAGE-A3 and NY-ESO-1 proteins on their cancer cells. The vaccines contain harmless parts of these proteins allowing them to show these proteins to the immune system. It is expected the immune system will 'learn' that these proteins are foreign to the body. The immune system should then attack the proteins on the cancer cells, killing them. It is expected the vaccines will help the chemotherapy and immune checkpoint inhibitor to work better. This is a first-in-human clinical trial which has two stages: * A 'Safety Run In' stage where six evaluable patients will receive the trial vaccines with standard of care treatment to confirm they are safe before opening the next stage. * A 'Rolling Recruitment' stage consisting of two cohorts: 1. NSCLC Randomisation Cohort of approximately 80 patients with NSCLC will be randomly allocated by computer (randomised) to one of two groups (arms). Patients in Arm A will receive the vaccines with their standard of care treatment and patients in Arm B will continue with their standard of care treatment alone. There is a 1 in 2 chance patients will receive the vaccines. 2. Squamous Oesophageal Cancer Cohort: Approximately 17 patients with squamous oesophageal cancer will be recruited to receive trial vaccines with their standard of care treatment. The main aims of the trial are to find out: * More about potential side effect of the vaccine and how they can be managed. * Whether the vaccines with standard of care treatment are better at shrinking NSCLC than just the standard of care treatment alone. * What happens to the vaccines inside the body.