We did the following to resolve the issue:
- Log out of Office 365 - just log out of any one of the programs;
- Cleared the cache credentials - see the control panel for the Windows Cache Credentials and then deleted anything to do with Microsoft Office 365;
- Uninstalled Office 365;
- Restarted the computer and ensured that no Cache Credentials were left;
- Re-installed Office 365.
This was the only way in which we could resolve this problem. It took some time.