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Yeah, back when I was really into them I had one but not a full set like yours, just the razor. IIRC it is a model 15 ? Anyway ..... it was a great shaver. I still have the USA counterpart, also an...

Bull dog was a 3 piece, not a twist to open .... A.K.A. TTO

Go to this website here and you may be able to find out more specific info on your set.

Edit; Found your set on his website. He says 1936.
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I believe you have a British Gillette Aristocrat. The British Gillettes do not have a date code but because of the open comb guard I would suspect it is a 1930s piece. Looks to be a rhodium plated...