You cannot do the routing you want. However, remember that SQ flies to other cities in Europe other than London. CPH - FRA - SIN - PVG may be an acceptable routing.

As an alternative ... you can do what I did earlier this year to go to Shanghai and HK. Book a ticket Copenhagen - Frankfurt - HK (I came back via PVG, also on LH), and buy yourself a cheap £50 single from EDI to Copenhagen to start the trip. Coming back, throw away the Frankfurt - Copenhagen leg and buy yourself a FRA - EDI cheapo single.

Its a fantastic deal - you save 20,000 miles, and you pay less on the 'cash' bit as well - which covers the cost of the 2 singles you need.

Also, doing F on Lufthansa, you get to visit the First Class Terminal in Frankfurt, which includes a private chauffeured car to the plane. Very, very cool indeed.