Moderator, Iberia Airlines, Airport Lounges, and Ambassador, British Airways Executive Club
Join Date: Feb 2010
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You can use the First Wing AND leave your bags through checked. In the GLA-MIA direction that would be bonkers. In the MIA-GLA direction it would sensible and what CWS and many others do every time. Your baggage will follow via the magic of Ready to Fly whenever and however you get to T5 airside.
GLA probably would give you the option to short check, though strictly speaking it would need an overnight option. In the MIA-UK direction they probably won't give you the option. The message is actually to cover very different circumstances to the one you are asking about, such as when there is a codeshare or other airline mid sector and they then endeavour to enforce their policies.
[Nice to see a longstanding typo has been corrected on BA.com!]