David,
If you believe that Brexit will prevent you visiting other EU countries, I trust that you will be pleasantly surprised by the outcome. You may be prevented from settling in other EU countries, but that is a different matter entirely.
You seem to think that to have this right taken away by people too lazy to make use of it only those who never travel abroad have voted Brexit. In my case, and I would assume for millions of others, this is just not true.
I have visited much of Euprope, both recently, and before we joined the 'Common Market'. Getting in to Europe was no harder pre the common market than it is now.