Yes (assuming the flight leaves before 3.15pm - I know BDA is a late one...)
http://www.gatwickairport.com/at-the...fore-check-in/
British Airways
North Terminal
Opening hours: 16:00 - 22:00.
Eligible flights: All next-day flights departing before 15:15. Use the self-service check-in kiosks, then deposit your baggage at the fast bag drop in zone A.