One argument by the Leave campaign that has resonated more than any other in the EU referendum debate is that the UK should take back control. The EU is undemocratic, this argument goes, and its powers should be restored to British MPs, who can be held to account by voters. A rousing argument to be sure but how reasonable is it?

Those who view the EU as undemocratic can point to the Union’s persistent disregard for the will of the people as expressed through European referendums. In 1992, Danish voters rejected the Maastricht Treaty before being asked to vote again. A similar sleight of hand happened in Ireland in relation to both the Nice and Lisbon Treaties.

In Greece, last year, voters sent a clear message that the conditions attached to EU loans were too harsh. Yet, within weeks of this referendum, the Greek government had signed up to yet more EU loans under even harsher conditions.

At least those countries had the semblance of a say, Leavers might argue. Pressure for a referendum on EU treaties has been building in Britain since Maastricht. However, successive Prime Ministers withstood such pressure until David Cameron reluctantly agreed to hold today’s in-out vote.

Politicians’ aversion to referendums forms part of a broader narrative about EU elites’ determination to press ahead with European integration in the post-Maastricht period in spite of popular concerns.

Over the last two decades, the EU has launched the euro and created common policies in areas such as foreign policy and justice and home affairs. During this time, popular support for the EU has fallen. In 1991, polls suggested that more than 70% of people saw their country’s membership of the Union as a good thing. By 2011, this figure had fallen below 47%.

The UK is less exposed to this political contradiction than other member states because the British government has negotiated opt-outs from the euro and from large swathes of justice and home affairs. Nevertheless, it finds itself a member of a club that has acquired significant new policy-making powers over the last two decades.

Against this backdrop, a vote to leave the EU today might be viewed as a way to break these pernicious political dynamics and reboot British democracy. But such reasoning is too simplistic. For one thing, it deflects the EU’s problems to unelected elites in Brussels rather than the true power brokers: the national governments of the 28 member states.

True, the EU counts among its institutions a number of independent bodies. The most clear cut cases are the European Commission and the Court of Justice. But independent institutions are a feature of many international organisations, as in the Appellate Body of the World Trade Organization.

The EU stands apart from other international organisations not because of its independent institutions but because of its democratic ones. The European Parliament is the world’s only directed elected transnational legislature. Only Mercosur has come close to considering such an arrangement.

No democratic fig leaf, the European Parliament now decides on much of the EU’s economic, social and environmental regulations in tandem with ministers from the 28 member states. In 2014, the European Parliament even played a decisive role in choosing the President of the Commission, increasing democratic accountability over this independent body as a result.

The problem for the European Parliament is that it is influential but also invisible. In 2014, just 11% of Britons could name their MEP. In the same year, only 36% of voters in the UK turned out for the European Parliament elections.

In need of reform though EU institutions evidently are, claims that these institutions are driving the UK towards deeper integration in Europe are plain wrong. Major decisions about the political direction of the EU are taken not by the Commission or the European Parliament but by the representatives of national governments in bodies such as the European Council.

The central political puzzle facing the EU is why the support of democratically elected national governments for European integration has not brought greater legitimacy. The answer lies not only with EU institutions but within its member states, which face their own deep-seated problems of legitimacy. None more so than in the UK, where trust in the country’s Parliament and political elites has been eroded by political scandals, policy failures and the decline of political parties. In a recent survey, 15% of Britons said that they trust Parliament. Just 11% expressed trust in political parties.

The British Parliament has not, as Leavers often argue, been disempowered by the EU. Under the UK’s uncodified constitution, treaty-making falls under the Royal Prerogative and so is a matter for the government to decide upon with limited involvement from MPs. But Parliament has broken from these traditions by exercising a decisive say over the UK’s membership of the EU. The decision to join the, then, European Communities in 1973 was approved via Act of Parliament and EU treaty amendments since have been approved in a similar manner.

In this sense, EU membership has empowered Parliament but the UK legislature no longer packs the democratic punch that it once did. As a consequence, successive governments have signed up to treaty after treaty with parliamentary approval but without fully legitimating such decisions. Today’s nationwide referendum, a seldom seen instrument of governance in the UK, is the clearest expression that the usual levers of legitimacy in this country are broken.

Can voters take back control today by voting to leave the EU? Yes in so far as a vote to Leave would remove the UK from a club that has pressed ahead with integration in spite of popular concerns about the European project. No in as much as the EU’s problems are not driven by undemocratic institutions in Brussels but by governments facing their own domestic political difficulties. The UK government has not, as many Leavers argue, lost control to the EU. It has, if anything, lost control to Parliament, which in turn has lost its traditional power to legitimate. Today’s referendum is an expression of this constitutional conundrum rather than a solution to it.

Dr Dermot Hodson is Reader in Political Economy at Birkbeck.