I recently purchased a foot switch for a standing lamp. The switch is rated for 1A at 125V.
I would like to use this switch with a low energy lamp (typically 10W or below) but with a 240V supply. Is this safe?
Likely you cannot - the insulation rated for 125 volts might fail at higher voltage and this might lead to an arc starting and causing a short. Also the circuit breaking capacity might be not enough for higher voltage, this can cause an arc starting when turning the switch off and that can overheat the switch and set it on fire. I strongly advise against trying this.
You can think of the Amp rating as rating the conductor, and the voltage rating rating the insulation. You can't compensate for inadequate insulation with a good conductor.
James, if you are in the US, there are not many 240V lamps available for residential use, especially like the Ikea store. Most standing lamps here in the US plug into wall sockets, 15A 120V. If that is the case then you can use a 125V switch. Since your lamp is 10W and "IF" it using 120V then it is using .08 amps (watts divided by voltage = amps, 10 / 120 = .0833) If all the above is true then the switch will be no problem. If you live where the lamp plugs into a 240V area, if it is like the US then you do not want to use a 125V rated switch because you will only be turning half the electricity off (120V A phase plus 120V B phase = 240V.
Also, using the math above, 120V X 1.5A = 180 watts.