Prime Minister David Cameron lambasts claims by the pro-Leave campaign that leaving the EU will bring sovereignty back to the UK.
He says that if Britain leaves the EU, you will end up with the "illusion of sovereignty, but not the power, you don’t have control and you can’t get things done".
That stands in contrast to Boris Johnson and Michael Gove – two top Tories who went against their boss and are campaigning for Brexit – who both seem to relish any opportunity to argue leaving the EU would enable the UK to regain control over its own affairs.
Their argument is based in the fact that as a member of the EU we cannot simply throw leaders out if we want certain changes, stemming from a conviction that power should be given to elected leaders who are answerable to the electorate, and an ardent opposition to institutions of the EU that sit above national parliaments.
But others challenge this view. This camp says that wouldn’t happen, because if the UK left the EU, it will still be subject to large amounts of EU regulations if it wants to retain access to the Single Market.
But as the UK wouldn’t have a seat at the negotiating table, some state that the UK would have less sovereignty as it would be bypassed in the decision making process and simply subject to it.
Of course, much of that will depend on the negotiations after the referendum. But even if you think Brexit would allow the UK to become unshackled from the EU, would it regain sovereignty?
For Kenneth Armstrong, Professor of European Law at University of Cambridge, people realise that the issues are really about power and influence in a world where no country is truly sovereign.
"Sovereignty belongs to an era where problems and their solutions were located in nation states. The problems the world faces now cut across borders and so the challenge is how best to harness the individual and collective powers of states to manage those problems," Armstrong says.
So, he says the choice is between trying to exercise power and influence on our own or through cooperation with other European countries.
In fact, there are lots of important things that the UK does on its own anyway like the NHS, education, social services. And in areas like policing and criminal justice, cooperation with EU countries can actually help the UK exercise power by ensuring that criminals that flee justice can be brought back to the UK.
"It is often said that if the UK were not a member of the EU it would have more control over the problems the UK faces. But the question is surely whether the problems are ones that can be solved by states acting alone," Armstrong says.
To pick one poignant example, he ponders: "Does anyone really think that the refugee crisis is a crisis that is better solved by states acting alone - each one putting up fences and sending refugees to another EU state - or by states trying to agree a common solution?"
Likewise, for Professor Stephen Weatherill, who specialises in European Law, the most important factor to analyse is power.
"As a member of the EU, the UK - like all the other 27 member states - has agreed to work within the structures foreseen by the Treaties: that means using the Commission, acting through the Council and the Parliament, relying on the Court," he says.
That means the UK uses the EU to address problems like climate change, security, migration and economic reform, including the need for guaranteed access to each others' markets.
"We do this through the EU, and not simply through our national capitals. That is because what we do in common, we do better - we have more power as a bloc of 28 than would apply if all 28 were doing their own thing. The EU, then, adds power - to the UK, to all the other 27 member states," Weatherill adds.
Professor of European Law at the London School of Economics Damian Chalmers does not agree. He says that legally, EU law restricts parliamentary sovereignty. The most practical effect of this is that UK courts will apply EU law over national law unless a parliamentary statute says otherwise.
"This restriction would go with Brexit so parliament would be formally able to do whatever it wanted. This possibility already exists under the British constitution but is practically impossible because of EU membership. However, the big question is how often this power to deviate would be used," he said.
"There are significant pressures pushing many UK laws to be aligned with EU law. Being outside the EU, we would not participate in the making of its laws but may decide to follow them as the consequences of not doing so may be unattractive.
"If this power to deviate was rarely exercised, the regaining of sovereignty might be seen as quite hollow. By contrast, if it was used a lot, it would secure significant self-government," he adds.
It may be an understanding of that fact that led Labour’s Alan Johnson, who is leading his party’s campaign to stay in the EU, to recently accept that it may be necessary to cede some sovereignty in order to gain from the European Union.
Indeed, in a globalised world, most nations make trade-offs on sovereignty.
Take membership of Nato, including an obligation in Article 5 that requires all members to come to the defence of fellow members. That implies a loss of sovereignty over deploying the UK’s troops, but one that is considered beneficial for national security.
Or consider membership of the World Trade Organisation, which means the UK is committed to certain supra-national regulations, a trade-off considered necessary for economic prosperity.
So, in the context of the EU, the UK is also making a trade-off. True, as Professor Anand Menon says, the concept of pooling sovereignty is meant to imply that states can do more together in practical terms, even if it implies a loss of formal, legal control.
And granted, Armstrong says EU membership does mean that our parliaments and courts cannot apply national rules that conflict with our EU obligations.
If the UK voted for Brexit, Weatherill says, it means it could pass all the laws on paper that it liked, with no regard to the other member states, no regard to the Commission, no regard to the Court, and so on.
But Weatherill continues: "It could pass a law saying climate change must stop. It could pass a law saying that Italy must share information about suspected terrorists with us. It could pass a law saying France must never let migrants reach Dover. It could pass a law telling Germany to trade with us on the terms that we want."
"And of course all this would be largely useless in practice. This is the loss of power – sovereignty if you want."
That’s because countries are interdependent and have to work with each other to address problems. Or in Weatherill’s words: "The UK exercises its sovereignty as a state by participating in the EU, and the idea is to acquire extra power by working in co-operation with 27 partners instead of trying to do it alone."