RoadKing‘s situation would be slightly different in that s/he would be connecting on separate tickets. I therefore appreciate their concern that their first flight, say BRU-LHR, might be cancelled whilst their second, LHR-OSL, might operate.
However, it’s likely that any such cancellation would take place days beforehand, and the operating carrier would make alternative arrangements (which may even include Eurostar) to get a passenger to LHR on time.
This would apply to any carrier, but I understand RoadKing‘s specific concern in this particular scenario.
In the case of a very last-minute cancellation (which is much less likely), travel insurance might have to be relied upon, as the airline would not even necessarily be aware of the complete intinerary.
A good travel insurance policy will cover passengers affected in such circumstances, but only when cover is taken out prior to the announcement of any actual industrial action, and then only up to the amounts stated in the policy documents. It will usually be the policyholder’s responsibility to actually rebook and then claim.
Personally, I would generally be of the opinion that there’s limited real risk of any disruption occuring and given the stated preference for BA and the desire to mantain Executive Club status, then I would book without too much concern.