Yes, there never has been an institution officially known as the "Common Market". The EEC (European Economic Community) was formed in 1957. This mentioned a "Common Market" (among other things) but if you read the Treaty of Rome (which formed the basis of the 1957 agreement) you will see that there was never any doubt that the ultimate aim was political union across Europe.
However, when Britain was given its own "in/out" referendum in 1975 (two years after we had joined) the government was a little sparing with the truth. In its pamphlet sent to every household to help them decide how to vote, among the concerns it addressed was this:
"Another anxiety expressed about Britain's membership of the Common Market is that Parliament could lose its supremacy, and we would have to obey laws passed by unelected 'faceless bureaucrats' sitting in their headquarters in Brussels."
The pamphlet then want on to fail to directly answer that question but one of the things it did say was this:
"The Minister representing Britain can veto any proposal for a new law or a new tax if he considers it to be against British interests."
Whilst that may have been true in 1975 it certainly is not now and for that very reason alone the UK electorate should have been asked for its permission before such a fundamental right was given away.
"The European Union was formed after two world wars to bring the nations of Europe closer together, create prosperity and prevent further wars"
I suppose one out of three main goals achieved in fifty-seven years is not bad. Of course it is highly unlikely that a major war would have erupted in Europe had the EU never been formed, but you never know. What is certain is that friction between some member states is now far greater since the introduction of the single currency (the EU's proudest achievement) saw half a dozen of its users slide into penury. I'm sure they were more than pleased to see unelected officials sent from Brussels to usurp the powers of their duly elected governments.
Member states will not be able to "make changes as they wish". It is a club of 28 diverse and disparate nations and they all have to agree to any major changes. Because they are so different there is not a cat in heel's chance of them agreeing to any meaningful changes and that is why Mr Cameron's promise to "renegotiate" the UK's relationship is so disingenuous. We're stuck with it the way it is and we're either in or we're out.
Mr Farage sees his party's recent success to be not the number of seats they have in the European Parliament (which has very little power). He sees the vote as a critical expression of the electorate's view on the EU. Not only in the UK, but elsewhere it is quite clear that huge numbers of people want to see radical change and they will not get that with any of the three (now possibly only two) main parties.