This work assesses the economic feasibility of adopting decoupled energy storage technologies in the UK, using a methodology to optimize the size of individual components for charging, storing and discharging energy. Such technologies, including pumped hydro and compressed air energy storage, are likely to become more important in the future energy system. In this paper we consider liquid air energy storage as a case study - a technology that has the potential to provide multiple balancing and ancillary services to the electricity grid, as well as to obtain revenues through energy price arbitrage. Based on the UK's half-hourly electricity spot price in 2015, the developed numeric model calculates the revenue streams of a liquid air energy storage system from providing reserve service and arbitrage every half hour. Results from the genetic algorithm give the optimal sizes for the liquefaction, storage and recovery units, to maximize the net present value and allow us to calculate other economic objectives. Our model results suggest that the profitability of a liquid air energy storage system can be improved by either introducing waste heat into the system or increasing system scale. The payback period could vary from 25.7 years to 5.6 years for a 200 MW system, with the use of waste heat ranging from 0 degrees C to 250 degrees C.