First, the call for a referendum on EU membership is a red herring, we have already done it, and the people of the UK voted to stay in way back in 1975.
http://en.wikipedia.org/wiki/United_Kingdom_European_Communities_membership_referendum,_1975
Second, we have not paid out billions of pounds to any EU country apart from the Republic of Ireland, this was done to safeguard UK investments in the Republic and to support one of our most important trading partners.
We have paid no money into Greece, that is purely a 'Euro' problem, and therefore has nothing to do with us, we are not part of the Euro.
We underwrote £6bn of Portuguese debt, this means that if Portugal defaults, very unlikely, we may have to pay out on the £6bn, but no money has been given to Portugal at this stage, the Portuguese ecomony is important to the UK as we are net exporters to Portugal, so that nation remaining solvent helps pay our deficit.
Our deficit dwarfs anything that the Greeks, Portuguese or the Irish have, to claim that these deficits come from burning the candle at both ends is true only to a point, and could be levied at the UK more than it could at the Republic, Portugal or Spain, we were spending money based on USA investments that had no actual monetary value, the collapse of these investments caused the run on UK and worldwide banks that lead to the credit crunch, our fault for having a 'deregulated' banking system. So I cannot see how this has anything to do with EU membership.
The Greek finances have been in tatters for years, well before they joined the EU, they have always spent far more than they make, sooner or later the Greek economy was going to collapse, and one way or another EU membership or not, something would have to be done.
Illegal immigration, there is no illegal immigration between EU states, you can go and live in Estonia, Greece, France, Spain and Poland just as easily as those people can come here, withdrawl from the EU is unlikely to change that, free trade agreements would have to be set up with individual states, or prices of goods from EU countries would soar as tariffs were put in place, do you really want to be paying £10 for a Spanish orange, as part of these free trade agreements you can bet your life we would have to agree to a free exchange of labour. Such things existed long before we became a member in 1973. There has always been free movement of people between the UK, Republic of Ireland and some of the Scandinavian countries.
Fishing quotas, withdrawl from the EU would not make any difference, we can only catch what fish are there, the quotas apply to non-EU countries as well by international trade agreements (Iceland and Norway), we would still need to be part of that or we simply would find our fishing ports blockaded, anyway do you really want to fish the North Sea until there are no fish left in it?
The poster who mentioned Human Rights, the Human Rights Act has nothing whatsoever to do with the EU, it was UK legislation passed in the UK parliament, and to use this against the EU is nothing more than a fraudulent arguement.
We do more trade across the borders of the other EU member states than we do with any other nation of Earth, to remove ourselves from that would cost the UK far more financially than continued membership does.
I would also have to pick up on your claims about the 'vast majority', there is no vast majority, there is no national call for us to leave the EU, it is an invention of the media and and invention of Tory backbenchers who like to blame others for the fact that their policies simply are not working. UKIP exists, if people in their millions really wanted out UKIP would be the most popular party currently in the UK, and if the vast majority wanted out, do you think either Cameron or Milliband would seriously ignore it, they would both be calling for it, it would be Labour Manifesto pledge number 1 to use to get back in power.
Politicians need to be elected to keep their jobs, Tory, Labour and Lib Dem marginal MPs, and currently that is a large number of them, want to keep their jobs, this people would be campaigning hard for a referendum if they thought it would help them keep their seats, and apart from a small number of Tory and Labour MPs that is not happening, that silence says an awful lot.
If such a referendum was called the debate would begin and to be sure the nonsense that is often blamed on the EU would be exposed for what it is and the chances of the UK withdrawing by the time the vote came round would be very low indeed. Your resounding no would be disappearing faster than snow in July.