Future changes to the UK’s energy system, specifically radically increasing the deployment of renewable energy sources at all scales, will require much more flexibility in demand to ensure system stability. Using dynamic building simulation, this paper explores the feasibility of using thermal storage to enable flexibility in heat demand over a range of timescales: diurnal, weekly and seasonal. Time-varying space heating and hot water demand profiles for four common UK housing types were generated, accounting for different occupancy characteristics and various UK climates. These simulated heat demand profiles were used to calculate the necessary storage volumes for four heat storage options: hot water, concrete, high-temperature magnetite blocks and an inorganic phase change material. The results indicated that without first radically improving insulation levels to reduce heat demands, even facilitating diurnal heat storage would require low-temperature, sensible heat storage volumes well in excess of 1000L, in many cases. Storage of heat over more than a few days becomes infeasible due to the large storage volumes required, except in the case of dwellings with small heat demands and using high-temperature storage. However, for heat storage at high temperature, retention of heat over longer time periods becomes challenging event with significant levels of insulation.