If it's invol the lack of D class shouldn't matter. If a flight is cancelled, BA should just book the OP on one of the other LHR-SIN flights that day. I expect the OP is using the cancelled flight to get some crazy routing and fly some extra miles. (Apologies if this isn't the case, but I cannot believe LHR-HKG-NRT-SIN is the only routing available this far out).

Anyway, I wouldn't let this wait until you're in ICN. There is lots of potential for things to go wrong, so make sure to get the ticket reissued at least a few days in advance.

If you transfer in the US, it won't matter much if your luggage can be checked through, as you will need to collect and recheck your luggage anyway.