In this work we consider the problem of how to best allocate a limited supply of vaccines in the aftermath of an infectious disease outbreak by viewing the problem as a sequential game between a learner and an environment (specifically, a bandit problem). The difficulty of this problem lies in the fact that the payoff of vaccination cannot be directly observed, making it difficult to compare the relative effectiveness of vaccination on different population groups. Currently used vaccination policies make recommendations based on mathematical modelling and ethical considerations. These policies are static, and do not adapt as conditions change. Our aim is to design and evaluate an algorithm which can make use of routine surveillance data to dynamically adjust its recommendation. We evaluate the performance of our approach by applying it to a simulated epidemic of a disease based on real-world COVID-19 data, and show that our vaccination policy was able to perform better than existing vaccine allocation policies. In particular, we show that with our allocation method, we can reduce the number of required vaccination by at least 50% in order to keep the peak number of hospitalised patients below a certain threshold. Also, when the same batch sizes are used, our method can reduce the peak number of hospitalisation by up to 20%. We also demonstrate that our vaccine allocation does not vary the number of batches per group much, making it socially more acceptable (as it reduces uncertainty, hence results in better and more interpretable communication).