The study is designed to determine the safest dosage of pembrolizumab to be given in combination with chemoradiotherapy and brachytherapy for patients with locally advanced cervix cancer. The study will be run at the Royal Marsden Hospital only and is open label so both patient and doctor will know what treatment patients are receiving. Patients will receive pembrolizumab in combination with chemoradiotherapy and brachytherapy. Patients will be tested against 2 dose escalation levels (Dose Level 1/2). An initial dose of 100mg of pembrolizumab will be implemented. If dose limiting toxicity is not observed at this dose, pembrolizumab will be escalated to 200mg. A minimum of 3 patients will be required at each dose level. A minimum gap of 1 week should be left between the recruitment of the first and second patient in a new dosing level to mitigate against multiple patients suffering from any acute toxicity.