1. A method of switching an integrated circuit from an operational state in which data processing instructions are executed using an instruction pipeline to a power saving state in which execution of said data processing instructions is suspended, said method comprising the steps of: receiving a power down trigger event to trigger a switch from said operational state to said power saving state; completing at least some partially executed data processing instructions pending within said instruction pipeline and preceding within said pipeline an instruction at a restart point; and storing within storage cells of said integrated circuit state data defining a processing state of said integrated circuit which can be restored to said integrated circuit and execution of data processing instructions restarting from said instruction at said restart point; wherein upon switching from said operational state to said power saving state a main power supply operable to supply electrical power to said integrated circuit is disabled whilst a storage cell power supply operable to supply electrical power to said storage cells is maintained such that power consumption of said integrated circuit is reduced.