Of the other two alternatives, There was not a television set in my room" works although it's a little bit stilted, but I don't think anyone in BE would say "...not any television set".I know "There was no" is the correct one. But when we negate plural countable nouns we have two options.
To negate the sentence "there are some televison sets in The US." We can say either "There are not any/no television sets in The US."
But To negate the sentence "there is a twlevision set in my room.", is there only one way? Is there another way to say "there is no television in my room."