There certainly does appear to be a fair amount of discretion here but I would certainly never EXPECT baggage to interline if travelling on two seperate tickets – sure, ask about it but don’t expect it to happen. It did work out for me recently when I checked in with Bangkok Airways in Phnom Penh and they checked my bag through to the UK with BA, even though this was not a code share flight (some are) and I had two tickets. On the outbound, I had not been able to check my bag through with BA – as it happens, a tight connection in LHR meant my luggage did not arrive in BKK but BA there did send it on to Phnom Penh the next day.
However, last week, I was travelling GLA-LHR-SIN-KUL with BA and MH and we could not even get a through ticket at a sensible price, let along interline baggage, even though this itinerary was all oneworld.
In the old says, bmi rarely interlined from UK regions on to fellow Star airlines (GLA-LHR-BKK with TG, for example) because, it was explained to me, it was too costly for them to do so.