The use of energy storage devices in homes has been advocated as one of the main ways of saving energy and reducing the reliance on fossil fuels in the future Smart Grid. However, if micro-storage devices are all charged at the same time using power from the electricity grid, it means a higher demand and, hence, more generation capacity, more carbon emissions, and, in the worst case, breaking down the system due to over-demand. To alleviate such issues, in this paper, we present a novel agent-based micro-storage management technique that allows all (individually-owned) storage devices in the system to converge to profitable, efficient behaviour. Specifically, we provide a general framework within which to analyse the Nash equilibrium of an electricity grid and devise new agent-based storage learning strategies that adapt to market conditions. Taken altogether, our solution shows that, specifically, in the UK electricity market, it is possible to achieve savings of up to 13% on average for a consumer on his electricity bill with a storage device of 4 kWh. Moreover, we show that there exists an equilibrium where only 38% of UK households would own storage devices and where social welfare would be also maximised (with an overall annual savings of nearly GBP 1.5B at that equilibrium).