Buildings are amongst the world's largest energy consumers and simultaneous peaks in demand from networks of buildings can decrease electricity system stability. Current mitigation measures either entail wasteful supply-side over-specification or complex centralised demand-side control. Here, we investigate a new schema for decentralised, self-organising building-to-building load coordination that requires very little information and no direct intervention. We find that the theoretically optimal size for load-coordination networks can be surprisingly small, analogous to other complex systems such as coordination between flocks of birds. The schema outperforms existing techniques, giving substantial peak-reductions as well as being remarkably robust to changes in other system parameters such as the network topology. This not only demonstrates that significant reductions in network peaks are achievable using remarkably simple control systems but also reveals theoretical results and new insights which which will be of great interest to the complexity and network science communities.