There used to be a way for domestic flights but isnt so easy anymore. One easy way to check would be to phone and ask
Alternatively , check for flights on
http://matrix.itasoftware.com/cvg/dispatch/prego . Find one with the same fare for SIN-LHR r/t with SIN as the purchasing city; go into the details, then click on booking details, and you can see the fare breakdown including fare basis
e.g. for Feb next year, QF has a fare with base $998 r/t ... checking on ITA the fare basis for the $998 fare is VLSS1YSG
Dave