The simultaneous administration of SARS-CoV-2 and influenza vaccines is being carried out for the first time in the UK and around the globe in order to mitigate the health, economic, and societal impacts of these respiratory tract diseases. However, a systematic approach for planning the vaccine distribution and administration aspects of the vaccination campaigns would be beneficial. This work develops a novel multi-product mixed-integer linear programming (MILP) vaccine supply chain model that can be used to plan and optimise the simultaneous distribution and administration of SARS-CoV-2 and influenza vaccines. The outcomes from this study reveal that the total budget required to successfully accomplish the SARS-CoV-2 and influenza vaccination campaigns is equivalent to USD 7.29 billion, of which the procurement costs of SARS-CoV-2 and influenza vaccines correspond to USD 2.1 billion and USD 0.83 billion, respectively. The logistics cost is equivalent to USD 3.45 billion, and the costs of vaccinating individuals, quality control checks, and vaccine shipper and dry ice correspond to USD 1.66, 0.066, and 0.014, respectively. The analysis of the results shows that the choice of rolling out the SARS-CoV-2 vaccine during the vaccination campaign can have a significant impact not only on the total vaccination cost but also on vaccine wastage rate.