I did this route twice last year and on the way to GLA my bag was transferred in LHR no problem.
But each time coming back GLA - LHR - YEG, I had to collect my bag and re-check at LHR. It was a real pain and took a fair bit of time to collect and then go out to the Paddington Express to change terminals and check-in again.
The AC agent at LHR said he couldn't understand why BA couldn't check the bag all the way, but the girl in Glasgow was adamant that she couldn't do it.