Probably depends somewhat on what you mean by "power supply." My laptop runs on a 120V A/C power supply, but the "power supply" is a transformer that sits outside the laptop. So, up to the power supply (my definition, in this case) the voltage is indeed 120V, but beyond the PS (i.e., the wiring inside the device) it is 19V (and various lower voltages, too).
If you're device is an appliance that plugs into mains power, and you don't know for certain otherwise, the safe assumption is that it's 240V. But if you're uncertain, it's perhaps ill-advised to be modifying the device...
Does your device have the big UK plug, fused for 13A? If so, that is simply the PLUG standard.
You need to find the power rating of the device. What IS it? The photo looks like maybe a coffee maker (Or Tea - Sorry!)..
If the CURRENT used by the device is less than 10 amps, the typical small relay board that can be controlled by Arduino would be adequate. (This IS an Arduino control question? What do you want to accomplish?)