This paper seeks to quantify the mutual interactions of electricity, gas and carbon prices in the UK using a structural, co-integrated vector error-correction model, a methodology introduced by, among others, Pesaran and Shin and Garratt et al. This framework includes both long-run equilibrium relations and short-run interactions while modeling the prices of these three commodities as jointly endogenous. The model is estimated using data from Phase I of the European Union emission trading scheme. We derive the dynamic pass-through of carbon prices into electricity prices and the response of electricity and carbon prices to shocks in the gas price. While the gas price influences the carbon price, both of them drive the electricity price. Ultimately a 1% increase in the carbon price translated into a 0.32% increase in electricity price in the long run.