It should be clear to anyone that you cannot have a democratic UK under the current Treaties. Nice, Amsterdam and Lisbon certainly prevents that, and arguably parts of the Rome Treaty as well.
Restoring the UK’s ability to veto new EU proposals in the major areas that Labour surrendered would help, and would be a minimum requirement. It would still leave substantial jurisdiction transferred to the EU which makes it difficult or impossible for the UK to control its own borders, pursue its own welfare policy, control its own fishing and many others. To remedy this the UK would also need the capability to override Brussels and ECJ decisions where the UK Parliament thought that essential. There would then be a retrospective veto available for the worst cases.
A better and more realistic way of getting agreement to a new relationship that would work for us and them would be to define what the UK wishes to stay in. The business community seems to be surprisingly keen on all the rules and regulations of the single market when it comes to making any decision about the UK’s future. The UK could agree to belong to the single market, with rights to sit around the table and be outvoted on new proposals, whilst withdrawing from anything to do with borders, welfare, criminal justice, fishing and others.
The problem with all of this is twofold. The EU is well known to expand its jurisdiction. After a new settlement the EU would likely decide more and more things were single market with a view to ensnaring the UK in them. The EU has introduced qualified majority voting for many of these matters, so the UK would be back in the position of having to comply with things it did not agree with.
This shows why it will be very difficult to negotiate a new relationship that does restore UK democratic control, and why many will decide leaving is the easiest option. Leaving also means we will be £15 billion a year better off. Those who wish to stay in at any price have to explain why this is a bill worth paying, and tell us what might stop it going up too much in the future. As much of the rest of the EU in Euroland is going to have to send much larger transfer [payments from rich to poor, how do we avoid the UK being sucked into that system? The impact of a common policy o0f sharing on our fisheries should be a warning to us of what can happen when you let the EU run something for you.