With the signing of the Maastricht Treaty in 1992 Europe shifted focus from integration and inter-nation cooperation to the construction of a so called super-state. The European Union, which in the Maastricht Treaty replaced the European Communities, is not a "United States of Europe" as it is not a federation; it is a new nation-state.
As a nation-state structure, the EU's existence is directly contradictory to the continued existence of nation states as its members. By logical and political necessity Brussels would have to become the real, and only, capital of Europe. It was this inevitable future that the British people rejected. They were wise in doing so, because their vote may cause a turnaround and partial or (less likely) complete reversal of the super-state project.
If the British people had voted to stay in the EU they would have been part of a project where three things would have happened, each one serious enough to sink the entire continent, economically and socially: