I have a computer appliance that only accepts a 2-pin kettle power cord (UK plug type). I don't have a 2-pin available at the moment; only a 3-pin. The third pin that is missing is the ground connection. Would it be ok for me to use the 3-pin kettle? Both are 10 Amp, 240 V cables.
These are IEC 60320 standard appliance cables. This standard includes many different shapes for the connecting plugs and sockets, and they have been carefully designed so that unsafe combinations are physically impossible. It is safe to use this "C13" cable (10 amps, grounded, three wires) to power a device with a "C18" socket (10 amps, ungrounded, two pins), and therefore the connector shapes allow you to do so.
(Ironically, one of those impossible combinations is using a C13 cable to power an actual electric kettle; that's considered a high-temperature application and it requires a C15 cable. But you can use a C15 cable on a device designed for C13.)