Brexiters based the 2016 referendum on a series of myths: £350m for the NHS, imminent Turkish membership of the EU, and an easy deal that would keep us in the single market and take us out of it at the same time. These lies were long ago extinguished. But one unslayable old canard remains: the threat of an EU army.

Like a pub bore, it bobbed up again to corner the conversation this week after the signing of a Franco-German treaty, and Angela Merkel’s comment that this accord “contributes to the creation of a European army”. Brexiters quickly presented their evidence that remainers had lied about the risk and we were right to leave after all.

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The issue is a touchpaper for much of the anxiety underlying the leave vote, and so frequently ignites. An army invokes fears of domination and engulfment, the subordination of Britain to its historic rivals, and, anchored in memory, the unquenchable suspicion of a militarised European continent. But, like the anxiety, it exists only in the imagination.

Merkel and Macron’s Aachen treaty applies only to Germany and France, which remain both EU members and sovereign nation states. It is their prerogative to pool military capability if they wish. Likewise, in accordance with the Lisbon treaty, the EU decides all defence policies unanimously. If there ever were plans for a bona fide EU army, any member state could veto it.

But the larger point here is that the EU army of such lurid British nightmares cannot and will not emerge. There will never be any situation in which Brussels rules over a series of battalions and member states are compelled to deploy their armed forces against their consent. The main reason for that is the EU’s national governments hate the idea and always have.

Currently, the EU’s external action comes under the umbrella of the common security and defence policy (CSDP). It conducts more than a dozen overseas missions, ranging from civilian post-conflict monitoring and capacity building to military training. Perhaps its most ambitious project has been the anti-piracy mission in the Horn of Africa, Operation Atalanta, overseen (until Brexit day) from the UK’s military headquarters in Northwood. This, of course, reveals the other great myth of EU defence: that it has somehow been imposed upon Britain. In fact the CSDP began as a Franco-British initiative, and successive British governments have contributed both money and personnel to its operations. Nor has this enthusiasm waned with Brexit. The government’s 2017 security position paper expressly proposed future participation in EU missions, as well as involvement with the European Defence Agency and Defence Fund.

In recent years, the EU has sought to collaborate more widely on security and defence. Its principal innovation has been Permanent Structured Cooperation (Pesco), comprising 25 states on an opt-in basis. (The UK, alongside Denmark and Malta, opted out.) EU figures refer to Pesco as a “Schengen of defence”: a voluntary system for member states to integrate aspects of their defence if they choose. Projects include developing logistical hubs, equipment upgrades and rapid response teams for cyberthreats. It is not an army and nobody is declaring war.

The EU commission head, Jean-Claude Juncker, has also proposed an EU defence union in the next decade. Much like Pesco, advocates intend for it to boost individual countries’ capacities, pool resources and erase the need for member-state rivalry or duplication. Juncker has insisted that it would not impinge upon Nato. Nato’s secretary general, for his part, has welcomed the EU’s defence programmes, provided they do not seek to compete with his organisation. Juncker will leave office this year and have no power over the future of EU defence either way.

The problem with this debate is that its interlocutors cannot agree shared terms. While sceptics interpret enhanced EU defence through the language and lens of control, enthusiasts see only coordination. Such is Brexit. But army or not, strategies are evolving. As Donald Trump continues to undermine and blackmail Nato, the EU’s governments may deem closer military cooperation and collective defence no bad thing. If the Brexiters are desperate enough to block it, they should consider remaining.

• Jonathan Lis is deputy director of the thinktank British Influence