The zoo claims they are Barbaries, but all of the information I have been able to find quotes the zoo as a source.
I don't know anything of the background of those particular Lions, but this happens time and time again.
As pointed out earlier in this thread, there will be many Lions that contain a smidgin of Barbary blood in their ancestry, but from so long ago that its not really traceable any more. It still doesn't mean there couldn't be, somewhere in the World, Lions that are more directly descended from Barbaries, but if that's so, nobody seems to have discovered them yet.