Originally Posted by SFO777

Yes, you will have a problem. Unless you can legally enter Japan, you will likely be denied boarding at either CPH or LHR. You cannot arrive from and depart to the same country. Change your return to another city (like MUC) as you suggested and that should work.

Originally Posted by CPH-Flyer

Indeed, the rules talk about a transit to a 3rd country. Some posts above is the story of a denied boarding from someone flying US-Tokyo-US due to the 3rd country rule not being fulfilled.