Microsoft have reported the following service degradation, as of 09:17, 24/01/19:
Title: Can't access email
User Impact: Users may be unable to connect to the Exchange Online service.
Current status: We've determined that a subset of mailbox database infrastructure became degraded, causing impact. We're identifying the next troubleshooting steps to remediate impact.
Scope of impact: Impact is specific to users who are served through the affected infrastructure.
Next update by: Thursday, January 24, 2019, at 11:00 AM UTC
Administrators can use their admin control panel to view the latest status updates: https://admin.microsoft.com/Adminportal/Home?source=applauncher#/servicehealth
Other sources: https://downdetector.co.uk/problems/office-365/map/