Yes, just as Trump's win has many in the United States questioning whether or not our electoral college system still works, the Brexit referendum has caused a tremendous lack of faith in that nation's electoral system. People there were shocked at the outcome of their elections. Now there's a widened inequality gap, showing that their fears were founded.
For more than half the voters of Britain, Brexit is considered a step in the right direction to help citizens of all income levels and social classes. It is to restore faith in what they consider a flawed system. The Brexit referendum concerns many, but is not shown to cause a lack of faith in the system.
The Brexit referendum reflects less the widening inequality gap and more the dissatisfaction of middle class and elderly British with the functionality of the European Union. Economic woes over the last fifteen year have ravaged the economies of many European nations and the EU has not demonstrated the ability to do much about the problem. The British people never fully accepted integration into the EU, as represented by their continued use of the British pound. It should not surprise anyone that the people of Britain do not wish to be tied to an economic system that is not serving the British people. The so called "inequality gap" did not start after the referendum, but before it.
The Brexit referendum has not caused a lack of faith in the system, because the people in the United Kingdom did not have faith in the system before. Brexit was a reflection of the people's will. It did not cause the lack of faith in the system. People do not want their lives to be controlled by a few powerful people, far away.