hi,
Your ticket probably says what the baggage allowance is for each sector.
Since this is award ticket, I would assume that they are a single ticket, and so the piece concept should apply for the entire journey. But, I don't know. Look at your e-ticket. somewhere in there it'll either say 20KG or 2PCS.
If this was a paid ticket, then it would depend on how they were ticketed. If they are all in the same ticket, then the 2 piece concept should apply. When they are ticketed separately, then there will be issues on the CPH-LHR sector noting that SAS can be a bit of a 'stick to the rule book' , so you should prepare. I am assuming that you have a stopover in CPH.
I am currently on a trip where the first and last leg are 20KG only sector, whereas the rest are 2PC (*A Circle Pacific) sector. All flights/sectors are on the same PNR, but are ticketed differently. Since I am traveling with only one bag around 20K.. it's not a problem, but if i had more bags and a stopover before the last segment, that sure would have created issues.
cheers!! enjoy CPH..