You are only entitled to one stopover per ticket, which means that you woud need 3 tickets:
1) LHR-SIN-BKK: zone 1-7: 30K+£202.50+tax
2) SGN-NRT: zone 7-8: 7.5K+£52.50+tax
3) ICN-PEK-LHR: zone 8-1: 26.25K+£180+tax
total: 63.75K+£435+tax
For 2) you could have SGN-NRT-ICN with a stopover in NRT for the same price enabling you to fly between NRT and ICN rather than go overland. AFAIK, there is no direct SGN-NRT on *A but you can do it via SIN or BKK.
For 3): there is no direct PEK-LHR on *A, but you could go via FRA on LH (or BKK/SIN/NRT on TG/SQ/NH respectively).
They may, however, baulk at the routing as going via PEK+ somewhere else is anything but the most direct route from ICN. If you have some flexibility in the ordering, it might be better to do NRT-PEK-ICN instead of NRT-ICN-PEK, as you could then do PEK-ICN-LHR returning to LHR on OZ. While not geographically the most direct route, it would probably remain acceptable as both PEK and ICN are in zone 8 and ICN-LHR is direct on OZ. This routing also allows you to route via ICN on SGN-NRT for 2) (need to check whether OZ flies to SGN, though).