[DomesticExtremis]

Are you sure you have the right USB cable (some cheap ones are charging only, not data)?
Which Distro of Linux are you using?
Depending on which distro/desktop, you might need to run a utility to see what devices are attached.
Try running lsblk and lsusb from a terminal window before and after you insert the cable. If it is recognised, the device should show up in the output.
On my Fedora machine, it just works - the device is recognised and a file manager window showing the data drive pops up.