I'm doing the Norway/Iceland DCL cruise in 2016 and have already decided to spend time in London before going to Copenhagen for the cruise. Believe it or not, it was actually cheaper for me to get a roundtrip ticket to Heathrow and then book LHR to CPH separately. Just be prepared for sticker shock when you book your hotel in London.
Yes, sticker shock is definitely true!! I'm beginning to plan my London trip and those prices are steep! Luckily, I'll have enough points for 5 free nights, which definitely helps.