Well, the UK didn't just vanish overnight, it's still geographically in the same spot, so business will continue. It has to. It's pretty much a given that it can't continue as normal though, since leaving the EU probably means the UK will leave the free trade zone. They could go the way of Norway, staying in the free trade zone without being in the EU, but frankly, that's a pretty miserable position to be in, as you still have to abide by all the rules and regulations set out in the free trade agreement, but you no longer have any say in defining the terms of agreement, since you don't have a vote in the EU council anymore. A bit of a mess really. In short, I don't want too be too pessimistic, but this might very well be a Pyrrhic victory for the Leave campaigners.
