These are long distances. As many have pointed out, flying eastwards will save some time.

I would also consider adding an overnight stop here and there: for example, LHR-DXB(Dubai)-SIN-NRT-SFO-LHR. Each of us will have his or her preference, but I'd take two 8 hr economy class flights punctuated by a night in a real bed over a 16+ hour journey in Business or First. (With a RTW ticket especially, such stops need not cost much more.)