It's worse than that, UK's current leaders purposely ignore the fact that EU member states have the same sovereignty as the UK and what they UK wants individually doesn't necessarily match with what these member states want individually. In all of this there are two issues, the lack of respect for EU's will as a whole and the lack of respect members states individually, the strategy to divide to conquer was also a poor calculation that from the start created mistrust.
Whereas I wish we could reverse this awful decision, may I remind you of how we got here. The UK joined a common market in 1973 which was a good thing for trade. It was sold as that to the UK people and fears of losses of sovereignty for political, economic and legal policies were largely allayed. So the 1975 referendum overwhelmingly voted for continued membership.
The EU however, were constantly pushing for further integration and expansion of the whole project. This came to a head with Maastricht in 1992. There was bitter rivalry in the UK (largely because of what was said in 1975). But Major managed to get it through the house. This is when real fears of ever-closer integration began and the notion of a Federal Europe with its own tax laws and Army etc. looked like a real prospect.
In truth, more rapid progress in that direction has only been hampered by dissenters of which the UK was probably the biggest. (This is why that deep down many in the EU are probably glad to see the back of us)
The Eurosceptics in parliament were starting to grow a lot more vocal and becoming a real problem, especially for the Tories.
From about 2004 with the inclusion of many Eastern European countries there was a sudden surge in net migration. This coupled with the 2008 crash and subsequent austerity caused many affected people to totally lose faith in any government to solve their problems and in many cases, look for someone to blame. It was the same in 1930's Germany when the far right used the crippling austerity to turn on the Jewish people. So in the UK, European immigrants became the reason why people were suffering. So when Farage and his crowd sold them the UKip line they bought it.
Cameron, in an effort to resolve the issue once and for all tried to get some concessions and reforms from the EU. But the EU's view is that the UK had had more concessions than any other EU member. This is true. And it is ironic that when the UK was in we were always looking for opt-outs and now we are leaving we want opt-ins. Nevertheless Cameron came home with nothing so had to call the referendum.
So here we are.
Any disrespect that you mention stems from the fact that the idea was sold as one thing and then turned into something else altogether.
The reason that so many people listen to Farage is that, sadly, on several of his pet points like the lack of democracy he is actually right.
The EU is far from perfect and there are many areas which have major problems.
But I would have much rather stayed in and tried to reform it. Although Cameron didn't get much, I still think we had a lot of influence.