They are both correct and both natural.
There _may_ be a very, very slight difference in emphasis. "Will there be only" emphasizes the uncertainty, "will there be... only one" "Will there only be" emphasizes the surprising or extreme nature of being reduced to one, "Will there only... be one."
It's a little hard for me to imagine a situation in which the sentences, as you've written them, ending on the word ""country," make sense in the real world, though. However, one could certainly say "Will there be only one country to leave the European Union?" or "Will there only be one country to leave the European Union?"