***Update at the bottom***
After searching for ages, I came up with only complaints online and couldn't actually find a solution... So I thought I would make one!
Remember the days of Windows XP where you could upgrade in so many ways? Windows Update, Slipstream, IT Pro Deployment pack... I really miss how easy Microsoft used to make things!
If you have a volume license edition of Windows 8, you will know that you can't easily upgrade to 8.1 without downloading the 8.1 ISO and performing an upgrade, or upgrading your own deployment infrastructure to support it.
Whilst having your own deployment infrstructure is best for large companies, for smaller companies, this is a real big PITA that you really should try to avoid if you can.
Microsoft have taken the decision that you can't upgrade to 8.1 if you have a volume license edition of Windows. Well... There is a simple solution... Don't use a volume edition!
In order to easily upgrade using the store, open an administrative command prompt, and from there type:
(This is a Microsoft Retail default key used by OEM/System builders to get through setup, it will not activate, but you don't need it to).
Once you have done this, run "wsrest" to delete the windows store cache and restart your computer.
After you have done this, Windows 8.1 will appear on the Windows Store and you can successfully upgrade to it.
Once you are on Windows 8.1, simply change back to a KMS edition via the volume license default codes:
c:\windows\system32\slmgr.vbs /ipk GCRJD-8NW9H-F2CDX-CCM8D-9D6T9
Then activate against your KMS host
And you are done!
Update: A lot of people are commenting here about activation failing and the key being blocked.
Please note, this is simply meant to be a way to upgrade 8 VLK edition to 8.1 without a reinstall. It is NOT a way to get Windows for free or bypass licensing.
Once you are upgraded, the step I gave above will reapply a default product key that is not able to activate - it is your job to target your KMS (or other) host and activate in the same way as you did before the upgrade. If you do not, Windows will act in an unactivated state (the same as installing without a valid key)