I have the same thing every time flying USA-UK. If you just get the mobile boarding pass, it'll say when checking in 'Your documents must be checked at the airport'. You won't be able to board until you see a BA agent. If you hang around the gate area they'll usually call you by name before boarding starts. In DFW, it used to be there were BA agents in the AA Flagship lounge that could do this, but that's not the case anymore. I always allow a few extra minutes to see the gate agent before boarding.

Departing London to the USA the same thing happens, but you'll get your documents checked before you can go through security (in the first wing, they can do it in the counter just before the security entrance, or sometimes send you to a desk).