I don't know if the Chelsea desks have the same scanners as they do at the CCR or not given over the past few months they've needed to see status vs just scanning the boarding pass to check. I assume the scanner probably allows any GGL at current, and they ask to check because of the newer instructions which aren't yet aligned with the system.
Assuming the above, if you're flying BA they can probably skip the convo and just scan and if it goes green they'll know you're permitted.
Anyway, not to re-direct the thread into access rules again, but if anyone does get access on a domestic do keep us posted as whilst there does seem to be a 'position' on it, it may at some point change or may lack policing as we've seen further up thread.