The Horse (Illustrated) was the journal of The Institute of the Horse and Pony Club, the precuror of the British Horse Society. I’m unclear about when this was first issued and when it finished. It probably began publication in the 1920s. How long it survived past World War II I do not know. 

Christmas, 1931, No. 10
Christmas, 1935, No. 26
Spring, 1938, No. 35
Summer, 1938, No. 36
Michaelmas, 1938, No. 37
Christmas, 1938, No. 38
Summer, 1939, No. 40
Michaelmas, 1939, No. 41
Christmas, 1939, No. 42
Spring, 1940, No. 43
Summer, 1940, No. 44
Michaelmas, 1940, No. 45
Summer, 1943, No. 56
Michaelmas, 1943, No. 57
Christmas, 1943, No. 58
Spring, 1944, No. 59
Christmas, 1944, No. 62
Spring, 1946, No. 67
Summer, 1946, No. 68
Michaelmas, 1946, No. 69
Christmas, 1946, No. 70