There is a Group Check-In desk in T5 specifically for this. It's in Zone G, which is just to the left of South Security, it's clearly signed. And machine free. Funnily enough I've rarely seen more than a few people there, unless there's something like a special flight like there was for the New Orleans ebay service.

If the TA puts your BAEC number in the booking, it might come up anyway at some point if you log in and go to My Executive Club. Your name may only be confirmed in the booking a week or so before travel.