I think we may be getting somewhere here.
When plugged into one of the mic/line inputs on the sound card, the speakers do still make the noise. Using the headphones into the amplifier rather than into the soundcard, the noise is present in the headphones as well.
I don't have such a cable at hand but I'll try find another mains cable for the amplifier to try, and then perhaps one without a ground to try temporarily.
Thanks for all the advice so far