Other than trial versions which have limited life there are no "free" versions of Windows. The upgrade to 8.1 from 8 is free but you still need the original license.
As has already been said the upgrade to 8.1 DOES NOT GENERATE A NEW LICENSE KEY. The original license is in effect and you only have the 8 key.
There are workarounds to get Windows 8.1 installed using the Windows 8 key but there is no guarantee that Microsoft would not prevent them being used, this is always the problem with any unapproved "trick".
Officially the only way is to install 8.0 and then upgrade to 8.1. As Microsoft would have preferred all systems to have upgraded to 10 and so not have this problem they are unlikely to have any desire to make things easier for those that stayed with 8.