If a Biblical preacher makes 10 predictions, and one of them comes true, is that a reason to shout from the housetops? I have talked about how the prophecy biz works before. The successes are trumpeted, and the failures ignored.
One particular theory of prophecy has the EU becoming the beast of Revelation. Since us English speaking types could never be a part of the beast power, as we are the true Israel, Great Britain had to leave the EU. But these same prophetic wannabes had some absolute epic failures over the years. In the 50's and 60's the Worldwide Church of God expected Hitler to return to Germany from his secret U-boat bases in Antartica . As it became more and more obvious that this was absurd, the meme changed to a Hitler-like figure would emerge. Names were suggested. Of course all of these suggestions have died now, so new suggestions must be made. Like the famous scene in 1984 where IngSoc 
switches allegiance from one competing "rival" superpower to another. History has to be changed retroactively. "We were never at war with EastAsia." In the same way, prophetic failures are conveniently swept under the rug.
I first ran across this when I started to collect religious colporteur literature, books and pamphlets sold door to door at the beginning of the last century. One in particular went on and on about the prophetic importance of the Ottoman Empire, which self-destructed, with help from the West, just a few years after the book was published.
Since Jesus said that even he didn't know the timing of his return, the underlying assumption that Jesus will return soon may be flawed. Don't get me wrong--it will happen. We just can't know when. But to point this out reduces book sales. The reason we have so much odd prophetic speculation is that is what people want.
So no, Great Britain leaving the EU does not have anything to do with Bible prophecy. Rather than strengthen the EU, it may end it. It may also be the end of Great Britain as it splits into three parts. Instead of a coming Superpower, the EU is more likely to experience civil war and race riots.
It is a mistake to look at current events and twist them to fit Bible prophecy. It will almost always eventually be proven wrong, as was the 19th/early 20th century claim of the prophetic significance of the Ottoman Empire