I've opened Illustrator and the left toolbar is gone. I've reset the workspaces, tried them all. Relaunched the software, rebooted the PC. The latest version on CC is installed.
From what I can tell from screenshots online, there should be a "Tools" option beneath the Control option. This makes me wonder if a plugin isn't loading correctly. The tools are available with keyboard shortcuts but I can't work without the toolbar.
In the end I've uninstalled the software, removing all preferences and plugins when prompted, then reinstalled through CC. It's fixed the problem so hopefully that's the end of it. Thanks for your suggestion anyway.