I'm not an expert, so am only commenting.
Copyright on photographs is owned by the photographer (unless they've sold or given away the copyright). If the BBC staff took the photo, The BBC staff owns it.
Wikimedia on the other hand has taken a stance, that all "faithful" reproductions of public domain work are also in the public domain. That's their opinion right or wrong.
This sounds like something lawyers could get rich on.
I'd err on the side of safe, believe the BBC. You can add a link to the page with the picture.
Oops yes Vince is correct it's the Trustees of the the British Museum, not the BBC. However the other information still applies.