DJS: You are 100% right on the demographics of the #brexit: Older and uneducated.
Muslim immigration, contrary to #brexit claims, has nothing to do with the EU since the UK refused to be part of the EU scheme for relocation of Syrian refugees. They also has the right to maintain their own borders because they are not part of Schengen. I believe many #brexit voters are not aware of this and believe the EU is causing immigration.
The main immigration problem affecting #brexit voters is the free movement of labor within EU. This means a Polish plumber has the right to work in the UK and many brexit voters believe this is destroying the UK economy and social systems, claims that has little or no basis in reality. Immigrants from the EU to the UK are younger, better educated and benefit the UK and is an important contribution to the UK GDP.
When the UK leave the EU they will be outside the agreement on free movement of labor. However to be part of the EU trading zone this WILL be a demand by the EU and most likely will be the case. That is, to have the same agreement as Norway, they must allow free movement of labor and pay their dues to the EU. Many #Brexit voters are not aware of this either, or believe the UK will be able to negotiate some special arrangement.
In negotiating such an arrangement the UK has far, far less negotiation power than the EU (the EU is half the trade of the UK) and EU has political reasons to demand the UK conform to conditions similar to Norway or stricter to prevent further fragmentation.
On top of that many EU citizens see the English as spoiled kids who has complained and had their ways for 20 years with special agreements and rebates and that it is about time someone put the foot down and showed them the door. In is in, out is out. For instance, the UK has stood in the way for further regulations on the financial markets which is very unpopular in the rest of the EU. In local media I have seen "crazy girlfriend" used to describe the UK.