Upvote:1
Yes, unfortunately you will need to retrieve your bags and re-check them. I haven't had this exact scenario, but I have flown on a mixed Delta/British Airways flight before, where customs didn't even play into it (Cape Town to Johannesburg on British, Johannesburg to Atlanta on Delta), and was forced to re-check my bags.
I don't know if any airlines have arrangements to transfer checked luggage like that, but British Airways and Delta (as of January 2014) certainly do not.