Download the Windows 8.1 Pro ISO using the WindowsSetupBox.exe from
Upgrade Windows with only a product key - Microsoft Windows Help. Use the "Trick" to get the Windows 8 Pro Product Key to be accepted by the Windows 8.1 installer.
I found that the Windows 7 platform works every time, whether a real or virtual Windows 7 Machine (tested with 7 Home Premium 64 (real) and 7 Enterprise 32 Virtual on VMWare Player. I cannot get it to work on a real 8.1 update upgrade done via the Windows Store.
To install, I used the Windows 8.1 Professional product key (GCRJD-etc.) from here:
Appendix A: KMS Client Setup Keys
With VMWare Easy Install, where the product key and user details can be added at the beginning to run the install unattended, it takes about 40 minutes to install as a VM on a not very fast laptop with a Windows 8.1 host.
Activation should be done with your Windows 8 Pro product key.