Thanks Walter as always for your expertise! This is what we found out from Diageo's Archive Department (Black & White's parent company):
Thank you for your enquiry about your Black & White whisky bottle which has been forwarded to me here at the Diageo Archive. Using the photographs you provided, I have dated the bottle. The bottle would have probably have been produced between 1921 and around 1940. The neck label, as mentioned on the whisky.com forum, is missing; the neck label would have contained additional information, such as the royal warrant, which would have allowed us to narrow done the date further. The clear glass is rather unusual, making the bottle less common. The date given to you on the whisky.com forum, 1936-1939, puts your bottle in the later half of the period I mentioned above but this appears correct as your bottle does have a few subtle differences to the 1920s bottles in our collection. I have also found in the past that when he beats me to a bottle dating ‘wchurst’ tends to be fairly spot on with his bottle dates!