The scandal of horsemeat – its being declared as beef and smuggled across borders and then into processed food – is sweeping Europe. According to the Financial Times a few days ago, the process involved "horse meat from a Romanian abattoir being sold to a French supplier by way of a Cypriot trader, and then passed on to a French food processing company before landing on British and French supermarket shelves". Since then the "horseplay" has spread to Germany and from beefburgers to lasagne.

What needs to be recognised beyond all the immediate hullabaloo is that the scandal shows just how illusory it is to imagine that Europe can function as a "common market" without all the red tape and constraints on sacred national sovereignty that Eurosceptics so ferociously decry. Production for the market requires regulation. And if we want to enjoy the benefits of a highly developed international division of labour – and they are real – then we need agreement on common rules between the trading partners.

Now, in principle, such rules could be established without pooling sovereignty. All you have to do is to get a legitimate representative of 27 countries to sign up to a common set of rules and have it ratified by 27 sovereign national parliaments. It is just that you then give each country a veto and a huge temptation to use it to play strategic games with the other 26 trading partners. And every time circumstances change, you need to get the 27 representatives together and to agree again. Such intergovernmentalism does not look likely to generate efficient solutions. And that is what you need to remember the next time you read about EU regulations running to thousands of pages. Even then you are not done: what happens if a country fails to apply the common rules? If they are to have any clout, supranational elements will certainly be necessary in the area of enforcement. All of which shows how fatuous it is to criticise, on principle, supranational meddling in national affairs and the associated loss of national sovereignty. (And no, this does not, of course, mean, that everything that Brussels imposes on member states is beyond reproach.)

The recent debate on the EU budget also clearly shows the limits of intergovernmentalism. Wherever unanimity is required, things rapidly descend into a zero-sum scrap in which national politicians are rated according to how successfully they have bullied their partners, and even serious newspapers score the event like a 27-way boxing match: Cameron – winner!; Merkel – winner!; Hollande – loser! The problem is that this obscures the real news, which is that the outcome is a budget plan that is completely illogical from the point of view of rationally addressing the challenges faced by European citizens.

A more striking, and encouraging, recent example, also comes from the food counter: fish. For decades, EU fishery ministers have regularly met and solemnly agreed to carry on overfishing Europe's territorial waters. They have cynically allowed even the excessive quotas they had established to be flouted with impunity. They would presumably have carried on their intergovernmental bickering until the very last fish had been caught: Le poisson est a nous! Nein, der Fisch gehört uns! I want my fish back!

Now the European Parliament has voted overwhelmingly for an ambitious proposal to prevent overfishing. It takes a supranational institution to do what everyone knows is the right – indeed the only – thing to do. (The bad news is that this proposal now will now be sent to the council – representing the member states – which will almost certainly water it down.) Here, too, Europe's media have largely failed Europe's citizens by not looking beyond the specific matter at hand and pointing out the bigger issue.

The tragedy is that when things don't work in Europe – and they often do not – the reaction of most people is to call for competences to be brought "back home". The reality is that it is the still largely intergovernmental nature of Europe that in most instances is what prevents it working effectively. When 27 countries defend national sovereignty they maintain it individually but lose it collectively. Everyone suffers from races to the bottom, free-riding, externalities and myriad other problems that require effective collective action. The euro area crisis is vivid testament to that. It is sensible supranational solutions that are required to address the prime concerns of European citizens. Not just meat and fish, but jobs, inequality, living standards, a sustainable future.