The UK plans to bring all greenhouse gas emissions to net-zero by 2050. Carbon capture and storage (CCS), an important strategy to reduce global CO2 emissions, is one of the critical objectives of this UK net-zero plan. Among the possible storage site options, saline aquifers are one of the most promising candidates for long-term CO2 sequestrations. Despite its promising potential, few studies have been conducted on the CO2 storage process in the Bunter Closure 36 model located off the eastern shore of the UK. Located amid a number of oil fields, Bunter is one of the primary candidates for CO2 storage in the UK, with plans to store more than 280 Mt of CO2 from injections starting in 2027. As saline aquifers are usually sparsely drilled with minimal dynamic data, any model is subject to a level of uncertainty. This is the first study on the impact of the model and fluid uncertainties on the CO2 storage process in Bunter. This study attempted to fully accommodate the uncertainty space on Bunter by performing twenty thousand forward simulations using a vertical equilibrium-based simulator. The joint impact of five uncertain parameters using data-driven models was analysed. The results of this work will improve our understanding of the carbon storage process in the Bunter model before the injection phase is initiated. Due to the complexity of the model, it is not recommended to make a general statement about the influence of a single variable on CO2 plume migration in the Bunter model. The reservoir temperature was shown to have the most impact on the plume dynamics (overall importance of 41%), followed by pressure (21%), permeability (17%), elevation (13%), and porosity (8%), respectively. The results also showed that a lower temperature and higher pressure in the Bunter reservoir condition would result in a higher density and, consequently, a higher structural capacity.