The biggest danger is that an exit from the EU will create a difficult to disentangle financial situation where England was a launching pad to the EU for many American businesses. An exit will force these companies to change the way they do business and adjust where their resources are located in order to maintain access to both markets.
The financial backlash to both EU and England is likely to be substantial. It prompts people that the EU is facing difficulties and further tells people that England is moving back into pro-nationalist economic stance. While it doesn't make sense to exit abruptly and now for England the catalyst is more cultural.
England always had its own sense of pride. It values its culture and its glory days as an important part of people's identity as both a nation and individuals. The split is seen by many as saying we are British first and Europeans second. We set our own policies and don't rely on the German dominated EU.
That has always been the funny thing about culture. Once symbols and history embeds itself into the psyche of people it is difficult to move away. While the days of severe conflict between England and Germany have long passed the idea of Us and Them has not gone away. Moving away from Europe is seen as moving toward national independence and Britain's destiny.