A detailed investigation of the interaction between natural gas and power systems is necessary, due to the increasing interdependency of these vectors, especially in the context of renewable generations integration growth into the grid. In this study, an outer approximation with an equality relaxation decomposition method is proposed to solve a mixed-integer non-linear problem representing the operation of coupled natural gas and power systems. The proposed coupled modelling of natural gas and power systems is compared to decoupled operational modelling. It is demonstrated that operating gas and electricity as a coupled system resulted in about 7% of operational cost savings. In addition, the value of gas-related flexibility options, including flexible gas compressors, flexible gas generation plants, and gas interconnections, to the operation of natural gas and power systems is quantified for a 2030 GB energy system. It is shown that if the natural gas and power systems are flexible enough, the operation of the systems in the decoupled approach is almost the same as the coupled model and therefore there is no need to reform the current energy market framework to make the systems fully coupled.