Hi Ian -
apologies for the slow reply - things have been a bit hectic in day-job land since the start of this year ><
To your question, this randomization is applied by NetworkManager, as a feature. See e.g. these notes
You can control this easily enough. Simply right-click on the network icon in the panel, and click on "Edit Connections...":
Then, in the dialog that appears. double-click on your wired Ethernet connection (this will probably show up as "Wired connection 1" or similar, unless you have explicitly renamed it). A further dialog will open. Click on the "Ethernet" tab, and in the "Cloned MAC address" dropdown select either Preserve (to copy the mac address through) or Stable (to assign a hashed address that will still be constant boot-to-boot):
Your initial device MAC address, as shown in the Device field, will of course differ from the above.
Once done, click Save, and restart your system. You should now find the eth0 mac address is stable across reboots.