No deal is better than a bad deal. That’s the phrase that got Theresa May her only applause line in during her tricky appearance in front of Jeremy Paxman last night, and the theme that the Conservatives hope will allow them to recover from their difficult fortnight and get them back on track in the election campaign.

There’s just one small problem: it’s not true. For a small peek at what “Brexit without a deal” would look like, take a look at the ongoing travails of British Airways customers, grounded for 48 hours after an IT outage and left with nowhere to go.

Now imagine that, but for every plane flying from the United Kingdom to anywhere in the European Union or the United States. Currently, British planes are covered by the Open Skies agreement – a transport agreement negotiated between the European Union and the United States. But if Britain leaves the EU without a deal, its right to participate in Open Skies will also end.

So it is hard to see how for anyone in Britain who likes flying to Europe or America – which as I understand it is an increasingly popular hobby – “no deal is better than a bad deal”.

To which of course you might say, and reasonably so, well, what if a bad deal doesn’t include British access to Open Skies? Then, in that case, no deal and a bad deal are pretty interchangeable, that’s true. But Britain’s relationship with the EU isn’t limited to the question of who can fly where.

If you sell or buy goods to the nations of the EU, or if you buy or sell goods from outside the EU that come to Britain via the EU, “no deal” means that your shipments will be stopped at ports, as there will be no agreement about the size of tariffs and what you can legally transport over borders of EU member states. Is no deal better than a bad deal? Well, sure, as long as you don’t need whatever you’re buying or selling urgently, or whatever you’re buying or selling doesn’t rot.

But perhaps if you don’t sell or buy anything from abroad, or intend to fly to the United States or anywhere in the EU, or have a job that is dependent on anyone doing any of those things, no deal is better than a bad deal. Well, sure, unless you work at or sell to a research institution or a university. What happens to cross-border research projects if there is an exit without a deal?

And that’s without getting onto the issue of the Irish border, which without a deal instantly becomes a hard border between Northern Ireland and the Republic.

Then there are the things which we could do without in the event of a deal that only covered the essentials of EU-UK relations – what you might call a “bad deal” in May’s phrase – but the government is not seriously trying to replace. For example, at the moment, EU food inspectors check hygiene standards not only in farms, abattoirs and factories in the EU but all around the world for Britain. EU inspectors also make sure that electrical goods meet European safety standards.

Now, these are of course tasks that the British state could do itself, but they would require a considerable increase in the amount the government spends, both on new staff and on computers. As the question of whether or not the parties’ promises are “costed” is currently the subject of fierce debate, it is worth noting that while there are no costings in the Conservative manifesto anyway, what there is even less of is any wriggle room to hire safety inspectors and dispatch them around the globe. Nor is there any detail about how the state will fund a likely expansion of its IT capabilities to adjust to life as a nation trading outside the customs union.

And there’s the rub. Forget Theresa May’s claim that Britain is ready and willing to walk away from “a bad deal” – as it stands, Britain isn’t even ready for what her government thinks a good deal is. We haven’t staffed up to deal with a greater volume of customs checks when we are outside the customs union. We certainly haven’t prepared for capabilities we might lose, like safety inspections.

No deal is better than a bad deal? Don’t believe a word of it.