There were two clues here - the first was the fact that these are "French" Bulldogs - whilst the second was that the card has a postcard back.
This set is described in our original Godfrey Phillips reference book (RB.13, published in 1949) as :
113. 50. "OUR PUPPIES". Fronts printed by letterpress in colour. Backs in black, with descriptive text. Issued 1936, in two sizes :-
A. Medium cards, size 60 x 53 m/m
B. Post card size, 128 x 89 m/m.
Now in our World Tobacco Issues Index, the entry reads :
"OUR PUPPIES". Nd. (30) ... P50-120.
A. Medium.
B. Postcard size and format. Without series title. Puppies, back format identical with Set P50-117.C
That set is "Our Dogs", showing adult dogs. This was issued later, in 1939, and was actually available in three sizes, small (a set of 36, and yes, they are in standard cigarette card size), medium (a set of 30) and postcard (a set of 30).
The sad thing about these sets is that we do not know who the artist was. There is a signature on our set, but I cannot decipher it. And Phillips sets are spectacularly absent from every article on cigarette card artists that I have tracked down so far. However someone out there may know this name, and if so please do get in touch.