I've done this all over Europe, without a lost bag, touch wood. I tend to judge the airport case by case, excuse the pun. So, I was happy to check through when travelling via: AMS, OSL, HEL, BRU, MXP; also BKK when connecting to CX or MH. On the other hand, maybe being overcautious, I personally chose not to check through at SOF and VCE (not many connections, so I preferred to pick up on arrival from QR, and then take it to BA check in myself) and ARN (terminal change)

You always do need to speak to the gate agent before your final BA leg (or they will page you) for them to manually add your baggage tag to the booking. I tend to do this proactively where possible to avoid the "walk of shame"