"The bread is not in the market" doesn't mean the same as "There is no bread in the market". The first tells us that some specific bread (for instance, "The bread I baked this morning" or "the bread I like best"). The second means that there is no bread of any kind in the market. My knowledge of Latin isn't good enough for me to know how those two meanings would be distinguished in Latin.
Indeed, I had the same problem: "There is no bread in the forum" corrected to "there is not bread in the forum." I am not a native speaker myself, but I have been speaking English for some thirty years now and count myself as a rather skilled speaker, but I would not use the second form (perhaps only if I inserted "any" between "not" and "bread").