Not BA, sadly, but on easyJet one time shortly before landing at Luton , a member of the cabin crew said something like

“Please remain in your seats until the seat belt signs have been turned off. We have a very tight turnaround at Luton today before our next flight, so would appreciate it if you could take any rubbish with you. Alternatively, you may volunteer to help us clean the plane by standing up before the seatbelt sign has been turned off”

It worked very well...