If you have the 8.1 ISO you can create an ei.cfg file for your edition of windows, this will bypass the requirement to put an 8.1 install key in.
Yup but ur need to have something that can edit iso file is you want to burn a dvd easyest way is to make a usb drive which is easy to edit.
So If you have a windows 8 key that can been used for 8.1
Download both installers from the
microsoft that means windows 8 and 8.1 installers then start the windows 8 one and put in ur key and start the download then a sec or 2 in to the download quit the program and then run the 8.1 installer and it will just download it

and then let u save an ISO file or make a bootable USB drive.
If you made a bootable USB drive put in back in the usb if u have taken it out and go in to windows explorer and go to the folder on the usb called sources and make a new text document called ei and press enter then find the file
and rename .txt at the end to .cfg .
Next open the ei.cfg with note pad and paste the following
[EditionID]
Professional
[Channel]
Retail
[VL]
0
This will bypass the check just install it now and enter your normal windows 8 key
For people using the DVD version who cannot install because its want and 8.1 key try this XHQ8N-C3MCJ-RQXB6-WCHYG-C9WKB this wont allow u to activate windows u must change your key in windows once installed some people on other forums say this key gets you in.
Hope this helps