First, there is a real possibility that Britiain will not exit the EU at all.
The referendum is actually non-binding in a legal sense. Parliament could vote to suspend it tomorrow. Another referendum could be held. The Privy Council could even intervene on its own authority.
Second, Britain has yet to invoke Article 50 of the EU charter, which would formally begin the separation process. Despite the insistent (and foolish) efforts of the French and German governments for Britain to invoke Article 50 immediately, they have not done so, and thus remain an EU member in good standing.
Third, there is a substantial body of evidence that a large portion of the "Leave" voters had no idea the consequences of their actions.
The areas that have gathered, or will have gathered by week's end, as many signatures as the original Leave petition include; Scotland, Northern Ireland, Wales, and London. In short, almost all of the U.K., save rural and smaller cities in England proper.
Northern Ireland is even holding talks with the Republic of Ireland to unite the island. Protest Northern Ireland frantically scrambling to join the Catholic Republic of Ireland, and receiving a tepid response, is something I never thought I would see in my lifetime.
The nation of Britain is disintegrating into its constituent parts.
Great Britain may never leave because there simply may not be a Great Britain any more.
Finally, Britain's elite are already seeking to mitigate the effects of the referendum. Even if they hold their country together successfully, Britain will almost certainly seek a treaty to retain their economic rights while gaining some control over their immigration process.
Let's not start burning the furniture yet. Britain was independent for most of the post-War period.
The current panic may be merely the flip side of irrational exuberance.