Daily gas demand in the UK is variable. This is partly due to weather patterns and the changing nature of electricity markets, where intermittent wind energy levels lead to variations in the demand for gas needed to produce electricity. This uncertainty makes it difficult for traders in the market to analyse the market. As a result, there is an increasing need for models of the UK natural gas market that include stochastic demand. In this paper, a Rolling Optimisation Model (ROM) of the UK natural gas market is introduced. It takes as an input stochastically generated scenarios of demand. The outputs of ROM are the flows of gas, i.e., how the different sources of supply meet demand, as well as how gas flows in to and out of gas storage facilities. The outputs also include the daily System Average Price of gas in the UK. The model was found to fit reasonably well to historic data (from the UK National Grid) for the years starting on the 1st of April for both 2010 and 2011. These results allow ROM to be used to predict future flows and prices of gas and to investigate various stress-test scenarios in the UK natural gas market.