I am connecting to a BD flight from an SK flight. They are on two seperate tickets. I would like to through check the bags so that I don't have to to lug them from T3 to T1- even though I have 4 hours between flights and can collect the bags and re-check them in (if my inbound is on time- touchwood

).
I know that BD will not through check in bags on seperate tickets, but unless BD has specifically told them not to do it, SK will do this for me (as they have done this several times in the past).
My questions are:
1. Is it possible to through check the bags or has BD told other airlines not to do it?
2. Will BD create any problems at the time of checking in at LHR if I show them my baggage tags, considering that I have a BD ticket originating at LHR?
Thanks in advance.