Co-location of energy storage with demand provides several benefits over other locations, while still being able to provide balancing services to the grid. One of these additional benefits is deferral of distribution infrastructure reinforcement, allowing increased load growth. This paper considers the potential of electricity storage for peak shaving on distribution networks, focusing on residential areas. A demand model is used to synthesise high resolution domestic load profiles, and these are used within Monte Carlo analysis to determine how much peak shaving could be achieved with storage. An efficient method of finding the potential peak shaving using electricity storage is developed for this purpose. It is shown that moderate levels of storage capacity can deliver significant demand reductions, if suitably coordinated and incentivised. With 2 kWh of battery storage per household, the peak demand at low voltage substations could potentially be halved. The effects of PV capacity, household size and C rates are considered. With 3 kW PV per house, 4.5 kWh of batteries could keep peak flows at the same level as before the addition of PV. It is also shown that 3 kWh of battery storage per household could allow provision of all heating from heat pumps without increasing the peak demand.