Originally Posted by Shareholder

With the exception of BD which just introduced new rules for connecting baggage, AC will tag your bags all the way through to Athens. Show the agent your second ticket and s/he will tag the bag all the way through so you will not need to pick it up at customs/immigration and re-check it with your onward carrier. However, when you check in for that onward flight at LHR [unless it is a STAR carrier, AC cannot check you in], be sure to mention you have a bag(s) checked in and give the agent the stub so s/he can input the number(s) into that carrier's system so it will be accepted onto the flight.

You can then do the same thing on the way back, but in reverse order. Just be sure to show AC the baggage receipt when you check in at LHR.

[BTW, doing a search would yield dozens of threads that answer this.]