Seems I have misunderstood the purchase and after my trial version expired I decided to buy the upgrade version (thought it would be the one as I already had there software downloaded and used as trial). Now I have purchased the upgrade software, but obviously I do not have the previous licence code!
How can I get it to work and pay the difference only? Or do I have to contact Adobe, cancel the upgrade version, wait for the refund and order afterwards the full version?
I think you have answered your own question. We are all just users like yourself. It seems that some people are getting confused about the upgrade version. The first time you purchase Lightroom you have to pay the full price. The trial version is actually the full version, it just has a time limiter on it. The upgrade version depends on a serial number from a previous version (i.e. Lightroom 3, Lightroom 4, etc.) as well as the serial number from the upgrade version to be activated. So it appears that you will have to negotiate with Adobe customer support to resolve your problem.
The LR software is the same. It is the first serial number you enter that tells LR whether or not to ask for a previous version’s serial number. In other words it is the serial number that is either upgrade or full not the software that was installed, which can be both.