Well at least it shouldn't have any effect on the EUR currency

It will dont worry. But will take lots time.
Most will suffer London, then UK then EU.
London will for sure, no mater which path UK will take or like Switzerland or like Norway or like, ... , lost economy center of Europe. Most likely Frankfurt will take it over.
Berlin, Paris, and Amsterdam all claim they will take over and become the new European trading centre. They might all get some increased business, but I don't think any will exclusively take London's place. London's too well established, and if there are other exits from the EU business could start flocking back to London.