5ish years ago, just after the QF/EK tie up started, I was flying LHR-xDXB-xLHR-PVG (BA-QF-BA).
The aircraft planned for LHR-DXB had a tech issue (inop fuel pump IIRC), causing BA to change aircraft to one inbound from SFO, thus delaying the flight.
BA also refused to check through to QF (this was prior to the PNR check through policy change, but even then, this was on the same PNR and ticket).
Between the departure delay, ATC delays and 'issues' with the DXB transfer desks, by the time I got to the DXB A EK lounge (without a boarding pass), the QF flight was about to board and I was misconnected leaving EK to sort it out. After they couldn't get through to LHR (BA, cause of problem) or HKG (CX, ticket issuer), they got through to QF in SYD who rebooked and a 24 hour delay in arriving at destination.
BAs excuse when claiming EU261 was "unexpected maintenance requirements are extraordinary circumstances", and no amount of debate would get them to change their mind, even citing court cases which determined that maintenance requirements, unexpected or not, are normal expectations of operating an airline and do not count as "extraordinary circumstances" didn't do anything.
Whenever BA gets an EU261 claim, they just pick a reason out of the first contact, pull out a form letter to back up that reason and refuse to budge. When dealing with BA and EU261, nothing short of a court order will get them to pay up.