Indeed LGW and EDI airports offer this to BA customers (these airports share owners). The only thing I note is that on the website it suggests that the facility is until 22:00 hrs at LGW - from seeing LGW late at night I am not certain that can be relied upon. LGW's final flight for BA is typically the late GLA domestic out around 21:15 hours, and so if planning on using this facility I would aim to be at check in no later than 20:30 hrs to be on the safe side.