Error 80070057 when attempting to update Windows Server 2012 R2

Once when I was updating some servers running the version of Windows Server 2012 R2 I encountered something odd; no patches appeared in Software Center or in the Windows Update panel, even though the server was several years out of date and definitely had applicable updates!

In WindowsUpdate.log I found the following error message repeating:

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The fix for this is to manually download and install KB2919355, which is the April 2014 update rollup for Windows Server 2012 R2. After this has been installed and the server has restarted, re-run your updates scan and updates will show up in Windows Update or Software Center.