Japan’s demand that Britain doesn’t jeopardise its large investments in our country won’t have come as a surprise to anybody who understands how the EU’s single market works. But they may come as a shock to David Davis, the Brexit secretary, who still doesn’t seem to get the basics two months after being in the job.

The bluntness of the Japanese government’s intervention – a 15 page document published on the foreign ministry website just before the G20 summit – shows it means business. Among the warnings are that Japanese companies might shift their European HQs out of Britain; that financial firms might relocate to other EU countries; and that pharmaceutical groups might move too.

This is not a small matter. Nearly half of Japan’s investment in the EU last year came to Britain. Companies like Nissan, Hitachi and Nomura have big operations here.

What may surprise Davis – and other Brexiteers – is that Japan is not just, or even mainly, concerned about tariffs. Last week, the Brexit secretary said he would try to negotiate tariff-free access to the single market – as if that would be enough to secure our prosperity.

But look at what Tokyo wants: EU workers to continue to be able to come here; financial services firms to keep their “passport”; freedom to provide other services across borders; our regulations to stay harmonised with the EU’s; the UK to remain a centre for clearing euros; the European Medicines Agency (EMA) to stay here; us to keep access to the EU’s research budget; and a host of other things.

All of these are part and parcel of the single market. Without them, our ability to trade and attract investment will be diminished – especially in services which make up 80% of our economy and which are not affected by tariffs.

When Brexiteers say that other countries manage to trade perfectly well with the EU, they ignore the depth of our relationship with the bloc which is, for example, roughly four times more intense than our relationship with the US. And it is not as if America is rushing to a deal with us. President Barack Obama reaffirmed at the G20 that its priority was to reach an agreement with the EU.

And before the Leave camp gets over-excited by the fact that Australia is keen to cut a free trade deal with us as soon as we are free to, remember that we trade 40 times as much with the EU as with our antipodean cousins. That means if we lost just 2.5% of our trade with the EU, we would have to double trade with Australia just to stand still.

Now look back at Tokyo’s wish list. How easy will it be for Theresa May to sell free movement to the hardliners in her party? Or the idea that Britain must keep its rules aligned to EU ones when the Leave camp has just promised to take control of regulations not lose control? And if the prime minister isn’t going to keep free movement, how will she persuade the EU to let us keep the financial services passport and access to its research budget, let alone clear euros and hang onto the EMA?

To achieve this May will need to be a magician. At the moment, she is evading tough choices. The most enlightening statement her spokesperson could come up with after last week’s cabinet away day at Chequers was that Brexit “must mean controls on the numbers of people who come to Britain from Europe but also a positive outcome for those who wish to trade goods and services.”

On the plane to the G20 summit, however, the prime minister did refuse to guarantee several pledges made by Vote Leave – including introducing an Australian-style points system to control migration, giving an extra £100 million* a week to the NHS, scrapping VAT on fuel bills and ending contributions to the EU budget.

May’s vacuous mantra – “Brexit means Brexit” – is wearing thin. One wit said it was like saying “breakfast means breakfast’. But some people want bacon and eggs for breakfast; others toast and jam; yet others muesli and yoghurt; and some want all of the above without paying a penny. Once the prime minister finally tells us what breakfast means, it won’t just be the Japanese who are unhappy.

* Vote Leave made various promises about the NHS. Its battle bus implied that there would be an extra £350 million a week for the health service.

** The data on trade with Australia was updated on September 7 to use 2015 figures

Hugo Dixon is co-founder of CommonGround – which is fighting for a fair and open society, and honest politics – as well as editor-in-chief of InFacts