I've done this before going LHR-SIN, just ask at check-in if they have any going... It's always worth it to me (and I always ask) as it is generally a cheap way of getting into WT+ (I think it was £175 to SIN) and then the chances of getting an Op Up to J is pretty high (I have about a 50% hit rate on WT+->J Op Ups)...
Availability will depend on how full WT+ is but I would say I've been able to do it maybe 30% of the time on LH flights - I try not to fly whY LH if I can avoid it but for non client related trips it's all my firm will pay for (hoping to do a paid for upgrade early next week to IAD - fingers crossed)