Mention concerns about the rule of law in certain EU countries, and people, even EU officials, automatically assume you are referring to Hungary and Poland. Without doubt, the state of democracy in both countries is worrying. Buoyed by strong electoral mandates, their populist governing parties are interfering with the independence of the judiciary and increasing state control of other institutions, including the media. But an equally worrying trend is less talked about. The decline in respect for the rule of law is happening elsewhere in the EU – indeed, it is an EU-wide issue and it has the potential to undermine the functioning of the entire bloc.

The World Bank's governance indicators show a deterioration in Bulgaria, France, Italy and Greece

Make no mistake, the European commission is justified in responding to developments in Warsaw and Budapest. Efforts there to undermine liberal democracy have been flagrant. The EU has responded by launching the so-called article 7 procedure, sometimes referred to as the nuclear option, as it can ultimately lead to a country being stripped of its voting rights. It has also pursued legal cases against the two states at the European court of justice.

But there is plenty of evidence from other member states – not to mention Brexit Britain, where Boris Johnson has clashed with the courts – that problems with the rule of law are more widespread.

The World Justice Project’s annual rule of law index and the World Bank’s worldwide governance indicators show a deterioration in other EU countries, including Bulgaria, France, Italy and Greece. In Greece, the conviction of the country’s chief statistician for sharing economic data with the EU that contradicted statistics previously used by the country to mislead international creditors has cast a shadow on the judicial system. In Italy, court proceedings take longer than almost anywhere else in Europe, and many criminals escape punishment because of the statute of limitations.

But institutional weakness and judicial independence are not the only aspects of the rule of law that the EU should worry about. The French authorities responded to terrorist attacks with laws giving them extensive surveillance powers with little judicial oversight, threatening the fundamental rights of individuals. Media independence, which is vital for holding governments to account, is also increasingly under pressure. Investigative journalists were murdered in Malta and Slovakia in 2017 and 2018 respectively, triggering political crises in both countries.

The EU should take a more structured approach to tackling so-called democratic backsliding than it has done to date and it should be using carrot as well as stick. It should begin by improving its methods of monitoring and early intervention. As Ian Bond and I argue in a new report for the Centre for European Reform (Democracy and the Rule of Law: Failing Partnership?), the rule of law should not be an east v west issue: all member states should be treated equally strictly. Ursula von der Leyen, the commission’s president, has taken a positive step in this direction by proposing an annual report on the state of the rule of law across the EU.

But if such a report materialises it must be based on transparent and verifiable data from a range of sources; it should not be a case of governments marking their own homework. The commission should make more use of information from the EU’s Fundamental Rights Agency, international groups such as the 47-nation Council of Europe, based in Strasbourg, and civil society organisations, some of which have to operate under severe pressure from their governments.

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If and when the commission has concerns about the rule of law, it should first give the government of the member state responsible the opportunity to address the problem itself. An effective early warning system would enable the commission to persuade governments to amend problematic legislation before it went on the statute book and became much harder and politically sensitive to reverse. But if a member state persists in violating the rule of law, the commission should not hesitate to ask the European court of justice to weigh in by ordering the country to suspend legislation or an activity while it considers its compatibility with EU law and principles.

The commission should also be prepared to tackle institutional weaknesses – such as court delays caused by a lack of judges – that are not always the result of malign actions by governments. The EU’s next long-term budget, which covers 2021 to 2027, should, for instance, allocate more funds to help train new judges. EU leaders should also put more money towards promoting public understanding of the importance of the rule of law – greater awareness of the issue will help breed stronger institutions.

The pan-European political parties, such as the European People’s party (EPP), also have a role to play in ensuring their national member parties uphold the rule of law. They should face sanctions themselves if they fail to expel national parties that flout the rule of law. It has been 10 months since the EPP, which is the biggest grouping in the European parliament, said it would consider the fate of Hungary’s ruling party, Fidesz, led by the country’s prime minister, Viktor Orbán, but it has yet to take any action.

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Critics often accuse the EU of being an elite project, imposed on unwilling populations. There is indeed a growing tension between what democratically elected governments in individual member states think their voters want them to do, and what their national courts and the EU institutions will allow them to do. But the EU is a community of law in which each member state applies EU rules, and trusts that others will do the same. Democratic backsliding by one EU member undermines this mutual trust, and threatens the functioning of the single market and the borderless area of freedom, security and justice.

For the sake of millions of European citizens, who benefit from these policies, the EU should do more to ensure the application of the rule of law throughout all the member states.

• Agata Gostyńska-Jakubowska is a research fellow at the Brussels-based Centre for European Reform