OK, they are using sport in a different manner than is used in the US, where it is used almost exclusively by game bird breeders to refer to the splash version of blue. Also, the genetic nomenclature in the link is wrong worldwide. The genetic symbol for barring is B, not Ba, and Bl is indicative of blue, not black. There is no specific nomenclature for black other than the various symbols for the base such as E (Extended black) E^R (birchen) etc. The lack of a blue dilution of black plumage would be bl+, but that does not ensure that there are no other genes that alter the black pigment, only htat there is lack of a blue dilution.
If British standards call for a heterozygous male (one copy of barring), then yes, you will produce some black and some doubled barred birds as well, depending on how you pair them up. US standards require males be double barred. I would check you standards to be certain. Even for a single barred male in the US, the barring in the 1st photo shown would not be correct. Our barring is supposed to be very crisp, and not wavy like in many of the photos in the links.