I've done this a few times recently, and presumably you too will be on a BAH in which case you'll have a BA flight number showing - which should be enough to be granted entry to Chelsea.

This has worked for me in the past, albeit last week I was mid-conversation about my inbound TransCon before I was cuddled by one of the Chelsea staff who told the desk I was a regular...not sure that happens to everyone, but be lucky!

M