You do realize these countries are already independent, right?

Precisely.

This isn't too hard to fathom really. There has been a groundswell of opinion for reforming the EU now for decades. Sadly the people who are best placed to do this (the commission) also possess the greatest incentive not to do so (they won't vote to dilute their own influence, and quite possibly the cuts in their salaries that will follow)

The commission has refused, blocked, and diverted all attempts at reform now for decades, whilst continuing to pursue their own power grab agenda. The people of Europe are slowly beginning to kick back against it. Frogxit won't be the end of the EU, but would rather herald in the beginning of a process of subtantive reform. It would be inevitable (unless Germany and Holland want to continue to underwrite the entire Mediterranean plus parts of the east)

At this point the UK could legitimately put a dead mans break on their own article 50 and say that the union they voted to leave, is currently going through a material transformation and that they're coming back to the table to see what emerges