Ultimately what has caused all this unrest across Europe is the transfer of millions of traditional manufacturing jobs to the Far East. This has left many areas feeling abandoned and a lot poorer, whereas successive governments have failed to re distribute wealth and new industries to compensate. These folk still have to cope with the high costs of UK/ European living but now with low paid warehouse and service jobs. Plus they have to compete with millions of foreigners for said low paid work. Result=Revolt. Giving money to the EU is seen as pointless.
But why is the transfer of these millions of jobs the fault of the EU and immigration? They're moving for cheaper workers/production costs. By your own admission immigration brings down wages, so while taking some job you could argue they're helping keeping the manufacturing here by driving down costs and providing an economic argument to the companies to stay here. That will only get worse as Africa becomes more viable and being in or out of the EU won't make a blind bit of difference.
If anything leaving the EU and thus making European markets less accessible and potentially affecting revenues and profits is likely to increase the likelihood of these companies moving abroad
Also the failure of government to restribute wealth and new industries where they're needed - again why is the fault of the EU? It's our own government deciding to build the student and education sector and protect the financial sector in the SE while not replacing manufacturing jobs in the regions. The EU money in grant is distributed far more to those regions than UK government spending on infrastructure etc. There is potential for huge growth in green technology and energy to replace things like the old factories and coal mining areas. The UK government have ignored this advice and pushed ahead with things like nuclear and fracking.
And these are the people that will have a much great say in things when we leave the EU.