For the most part, I have not had a problem with a bag transfer at LHR. The only exception was the first time I took my wife on a business trip. Of our two bags, one made it and one did not make. Came late the next day so not a big deal.

The exception would be if separately ticketed, of course. But with bags checked to their destination, unless there are extensive IROPS, there should be no problems.

Last time I was in LHR, my bag didn't even make a 2+ hour BA to BA transfer all within T5.

I'm heading to LHR in October on AA (via CLT) so really hoping they can at least pull that one off.