There are quite a few threads on this. From LHR and domestic stations no issue, there shouldn't be an issue at LGW (at least the self tag machines seem to have the option). Here are two of the many threads on this:
https://www.flyertalk.com/forum/brit...-allowace.html
https://www.flyertalk.com/forum/brit...signs-lhr.html
This is instead of an HBO allowance, not on top, so you can't do this with 3 bags and an HBO fare for example.
The messages about full flights still goes out, I had one earlier this week. If the OP is departing LHR I would just go to the end of the B zone desk, desk B16 where there is a special (and staffed!) queue for this.