The first one is saying "we would prefer you not to ((smoke or eat) in this store)", although it can also be read as "we would prefer you ((not to smoke) or eat) in this store", and only the use of large upper-case letters prevents "we would prefer you (not to smoke) or (eat in this store)".
Because parentheses aren't used this way in regular English, a better way of putting it would be: "in this store, we would prefer you neither to smoke nor to eat".
The second sign is saying "please (do not obstruct entrance) and (keep lane clear)", but again, it can be read a different way:"please do not (obstruct entrance and keep lane clear)".
In the first sign, the "not" applies to the entire clause, but in the second sign it only applies to the first term of the clause. It's only because we know that signs typically tell you not to do things you might other wise do that we can divine their meaning.
Perhaps Boolean logic should be taught more widely in British schools.