This is an interesting question so I did a little research. In Spicing up Britain: The Multicultural History of British Food, Panikos Panayi argues that before 1950, the concept of unique British food didn't exist. Only when people started visiting Indian, Chinese, Italian eateries was there any real desire to construct a British culinary identity. With the advent of canned food and industrialization, and the deprivations and rationing of WWII and the postwar era, this new identity lacked much of the tradition and sophistication associated with continental cuisines. The stereotype, however, most probably stems from classic Anglo-French cultural antagonism.

See also: James, A. "How British is British Food?" in Caplan (ed) Food, Health and Identity (Routledge, 2013)

Is this a stereotype of British food being awful or is it one of being bland? Ive never heard awful but i have heard bland, especially contrasted against much more "heavy" French dishes.