Not so much about these interline rules, but just had some 'fun' with baggage transfers/checking at LHR.
As part of my current RTW, I had OSL-xLHR-xDXB-xLHR-ICN.
2 nights in OSL, 22 hours (overnight) in LHR, then a QF10/QF1 turn through DXB then connecting onto ICN on BA. (my original plan for this trip was to have a day in London, get QF2 to DXB, have a day in Dubai, then get QF1 back to LHR to connect to BA17. QF wouldn't open the needed D space on QF2 - even though J and C were wide open - the waitlist didn't clear after 3 days and I ended up changing the plan)
MMB said different things depending on which airline I looked at, with some saying stopover in DXB, others saying stopover in LHR, others saying connecting at one or both.
Checking in with BA at OSL, they wanted to tag bags to DXB. I said to LHR. They checked me through to both QF flights and bags to LHR.
Arriving at QF check in at LHR, they saw that I had already been checked through for 2 of the 3 flights (to ICN). They tried to add the bags. While they had no issues checking me through to ICN, the system refused to accept the bags. At one point half the check in staff and the station manager were poking at it.
They worked out the issue was coming back through LHR and I had to put the bags into storage. The other option was checking bags to DXB, then having 3 hours to clear customs, collect bags, recheck and back to the flight.
I had wanted to avoid that because the UK Border Force agent I dealt with this time last year had issues with me wanting to enter the UK for 6 hours to collect bags from storage, get the train between T3-T5 and recheck with BA and sent me to secondary (thankfully I didn't have that issue again yesterday).