I don't know if its still the case but Swiss used to offer cheap fares to the Far East from LCY via ZRH (cheaper than to/from LHR when I flew with them). You would need to change airlines at HKG, BKK or SIN (or even NRT). As LX & SQ are both in Star Alliance you might get a codeshare via SIN - I haven't checked.
If you are booking separate tickets make sure that you have an adequate time for your connection. Otherwise you are on your own & face a very hefty bill if you don't make your connection.
Try ringing Trailfinders. They can often offer through fares with a change of airlines.
Last edited by Peter47; 7th Aug 2014 at 20:44.
Reason: Remove double line spacings