Before British voters went to the polls in June 2016, the institutions of the European Union were dismissed as “sclerotic, over-centralised and undemocratic”. Those same EU institutions are now portrayed as running rings around British negotiators. Here we find another – among many – of Brexit’s paradoxes.

This state of affairs stems from popular misunderstanding in the UK, as well as elsewhere, of how EU institutions actually work. It also reflects the fact that Brexit is a challenge to which EU institutions are better suited than their British counterparts. The loss of two senior ministers just days after the cabinet agreed on a new negotiating position makes British political institutions’ deficiencies all too clear.

Theresa May’s decision to put David Davis in charge of a new Department for Exiting the European Union (DExEU) in July 2016 helped to contain cabinet tensions in the immediate aftermath of the referendum. But it also weakened the UK’s negotiating position. Creating new government departments is not something that Whitehall tends to do well and DExEU has struggled to recruit and retain suitably qualified staff. It has had two permanent secretaries in two years.

Davis styled himself as a happy warrior in leading the British negotiating team. But his working relationship with the prime minister and EU counterparts was strained. He visited Dublin just once in his role as Brexit secretary. Remarkably, Davis spent just four hours in talks with the EU’s chief negotiator, Michel Barnier, in the first half of 2018. At home, rumours that Davis might resign surfaced regularly, until he finally quit. His departure, and that of foreign secretary Boris Johnson a day later, could yet generate sufficient momentum to topple the prime minister.

Johnson knows better than most British politicians how EU institutions work. His father was once an official at the European commission and even wrote a novel (which became a film) about a fictionalised commissioner. Johnson Jr’s understanding of the UK’s Foreign and Commonwealth Office (FCO) turned out to be less assured. His tenure as foreign secretary was marked by multiple gaffes on the international stage and a bit part on the European one. In spite of its vast experience in EU matters, the FCO has been sidelined in Brexit negotiations by DExEU and Downing Street. So much so, in fact, that Davis publicly questioned why Johnson had resigned over the cabinet’s new negotiating position when Brexit wasn’t “central” to the foreign secretary’s job.

EU institutions are far from perfect. They can appear remote and rigid. They have an infuriating habit of delaying crucial decisions until confronted with a sense of impending doom. And yet, by the standards of international diplomacy, the EU is both efficient and democratic. No other international organisation has a democratically elected parliament nor one that carries more weight than many national legislatures. None wields the same influence that the EU does at home or abroad with such clear rules for doing so and across such a wide range of policies.

The secret to EU institutions’ success so far in Brexit negotiations has been member states’ willingness to entrust responsibility to the European commission. Article 50 of the Treaty on European Union, which sets out the steps by which an EU member state can leave, gives the council of ministers leeway to decide who should be the union’s negotiator. Reports of a power struggle between the commission and the council over this role proved unfounded. The commission quickly appointed Barnier as its chief Brexit negotiator. EU leaders have always been clear that Barnier speaks for the EU27 as a collective.

Considered by some to be a controversial choice, Barnier proved to be a smart one. Having gained a good understanding of the Northern Ireland peace process during his tenure as European commissioner for regional policy, the EU’s chief negotiator was quick to grasp the economic and political repercussions of establishing a hard border on the island of Ireland. He has worked closely with the Irish government to address its concerns. Barnier has always made clear that there can be no backsliding on a backstop to prevent border checks between Ireland and Northern Ireland after Brexit.

The British government has also found it difficult to gain traction in the EU’s most powerful institution: the European council. This difficulty is not simply a matter of chemistry (or lack thereof) between May and other EU leaders. It reflects the fact that the UK, as soon as it voted to leave the EU, was excluded from the European council’s deliberative working methods. Meeting informally among themselves since 2016, the heads of state or government of the EU27 (that is: all EU member states except the UK) have spoken with one voice on Brexit. The European council, meanwhile, has severely restricted the time devoted to Brexit, making it difficult for May to bypass formal talks between her government and the European commission.

EU institutions’ “transformation” from bloated bureaucracy to a lean, mean negotiation machine may be an irony, but it is a bitter one – for three reasons.

First, it provides further evidence of how the UK’s vote to leave the EU was premised, in part, on a popular misunderstanding of how the EU works.

Second, the UK’s struggles to engage with withdrawal negotiations may strengthen the EU’s negotiating hand. But they will leave both sides worse off if a hard Brexit ensues.

Third, the unity of purpose that EU institutions have shown over Brexit is lacking on other pressing policy challenges, most notably over migration, eurozone reform and democratic backsliding in Poland and Hungary. EU institutions may be having a good Brexit, but this gives Europe no grounds for complacency.

A version of this piece was originally published on LSE Brexit

• Dermot Hodson is reader in political economy at Birkbeck College. John Peterson is professor of international politics at the University of Edinburgh