The only way to know for sure is to check the tag they put on your bag when you check the bag.

For example on a flight from ZUR-LHR-YYZ-YXU, at check-in with Swiss Air in ZUR, the agent told me our bags would not be checked through to YXU or even YYZ as 'your national airline Air Canada does not have an agreement for that. You will have to pick up your bags in LHR and re-check them with Air Canada.'

Then he went on to put a YXU tag on the bags. AT LHR, we went to baggage arrival and our bags did not arrive. Yup, they were transferred to our YYZ flight and yup, the were checked on through YYZ to YXU where we picked them up.

Since I had seen him put the YXU tags on our bags, I expected them to go through but nevertheless checked in LHR and YYZ just in case, given what he had said about them not going through. Trust but verify.

"Originally Posted by Yush
I wonder, though, why 2 BA agents told me, they would not check-through the baggage after looking at my booking." In my example Yush, the agent not only told me they would not check-through, he then appeared to contradict himself when he put the final destination tag on the bags!