Central to the vision of the smart grid is the deployment of smart meters that will allow autonomous software agents, representing the consumers, to optimise their use of devices and heating in the smart home while interacting with the grid. However, without some form of coordination, the population of agents may end up with overly-homogeneous optimised consumption patterns that may generate significant peaks in demand in the grid. These peaks, in turn, reduce the efficiency of the overall system, increase carbon emissions, and may even, in the worst case, cause blackouts. Hence, in this paper, we introduce a novel model of a Decentralised Demand Side Management (DDSM) mechanism that allows agents, by adapting the deferment of their loads based on grid prices, to coordinate in a decentralised manner. Specifically, using average UK consumption profiles for 26M homes, we demonstrate that, through an emergent coordination of the agents, the peak demand of domestic consumers in the grid can be reduced by up to 17% and carbon emissions by up to 6%. We also show that our DDSM mechanism is robust to the increasing electrification of heating in UK homes (i.e. it exhibits a similar efficiency).