Originally Posted by number_6
Not entirely. While the 10 day rule is bullet-proof and cannot be circumvented, you might be able to live within the rules. Buy a separate roundtrip ticket trans-Atlantic, breaking your RTW in North America for a while. This gets you back to LHR on the date you want, while the RTW does not do the last intercontinental flight until later (up to 1 year validity).
That's exactly the solution I was going to propose. ARN/GIB-xHEL/LON-SIN-HKG-LAX (-JFK?) on the RTW. Fly back to the UK on a separate ticket, then return to N. America later to pick up the remainder of the trip, and optimize your RTW. You could also use your remaining allowed 3 Europe flights (with 2 stopovers) in addition to any remaining N. America pieces when you do. Even if you rode on MaxJet (or used miles/copay/MFU) on the non-RTW transatlantic bits, the cost savings achieved by starting the RTW in Gibraltar or Sweden rather than in the UK would probably cover most of the difference.
(Note if you started in Stockholm you could make an easy connection in Helsinki to Singapore on AY, and get to try out AY's new J beds.)