I've found the answer from information posted by another user on the TechNet forum. Here is the link: Can't sign in to Microsoft Account.
I jumped straight to Step 4 in the reply marked as 'Solved', which was this:
Edit your registry
HKEY_USERS.DEFAULT\Software\Microsoft\IdentityCRL\StoredIdentities
Here, you will see the account that is giving you trouble. Delete (right click the email address and click Delete).
Settings, Accounts, add your Microsoft account back in.