We meet this evening, says Cassius to Brutus as they begin to plot the death of Julius Caesar. “Till then,” he adds, “think of the world.” It isn’t the most famous line in Shakespeare’s play, now given a pulsating, must-see new production by Nicholas Hytner at London’s Bridge theatre. But those words leap across the centuries and instantly engage with the modern mind.

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Think of the world. Not enough of us do. In Britain we are bad at it. British politics is particularly bad, and the British press, with a tiny group of honourable exceptions, is even worse. When we think of the world, the gulf between rhetoric and reality is immense.

Theresa May, arriving in China this week on a trade visit, is a representative example of the more general failing. She talks formulaically about something called “global Britain”. She writes, in the Financial Times, about a Britain “reaching out” to the world. She stands, as she did in Wuhan today, in front of a UK government logo proclaiming “GREAT Britain”.

The claims of British greatness and engagement are too often self-deceiving, and they were so long before Brexit. But Brexit both reflects the self-deception and raises the stakes for the gulf between fact and what is all too often fantasy. There is no deeper vision of Britain’s place there, and all too little realism either. It can’t be easy, admittedly, to bestride the world while assuring the travelling press pack that you aren’t a quitter.

The idea that Britain has become unusually active on the global trade front is itself a slippery one. May is beginning her second visit to China as prime minister. But Emmanuel Macron was there in January too, while Angela Merkel has made nine visits to China and counting. Germany exports five times as much to China as Britain does. The idea that Britain has somehow been liberated by the prospect of Brexit to seize pace-making status in the world is simply false.

In some respects Britain is not a global leader but a global laggard. Macron has only been president of France for eight months, but he has made six visits to Africa in that time. By contrast no British prime minister has set foot in any part of Africa since 2013. There is either no British diplomatic presence, or only a vestigial one, in some 16 African countries. Japan now has more embassies in Africa than Britain, and Germany more aid workers. How this all squares with a country that parades itself as open to the world – or as great – is hard to see.

There is more to thinking of the world than expanding our diplomatic effort. But more embassies, more diplomats and more people on the ground would at least be a start. In the past five years, however, the Foreign Office budget has been cut by 40%, at the very time the UK is leaving the EU. In Germany, by contrast, the equivalent budget has almost doubled. It now spends more than three times the British total.

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Britain should be thinking of the world a lot more realistically. Brexit is of course one reason for this. However much the pro-Brexit propaganda may pretend otherwise, it is increasingly clear – not least to diplomats and those who follow international affairs closely – that June 2016 was a watershed. It was when Britain took a decision that makes others think we no longer matter, and that Britain does not have to be taken as seriously as before. The departing German ambassador, Peter Ammon – a deeply experienced and benign diplomat – was right to warn us this week that we can’t take refuge from such realities in the heroic past.

But we also need to think about the world because the world order is changing. China spends $350bn in Africa because China can. Britain can’t. We are no longer a superpower. We are not the United States. Even the United States is struggling to be the United States. It is no longer in our gift to shape the destiny of China.

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But Britain is not Denmark or Switzerland, either. It has links, expertise, wealth, trade and assets that count in various ways. Its soft power – the language, the laws, the universities, the arts, the values, the respect for human rights – is disproportionate, despite Brexit. We should not put ourselves down as much as we do, but nor should we pretend we can shape the world on our own.

If we want to model ourselves on any country, it should surely be on Germany or France, which Britain so much resembles in so many ways. There are many differences, and they are not all in France’s or Germany’s favour – we’ve got Shakespeare, for one. But together, and in spite of all, we can be the future of Europe, even if not of the world.

• Martin Kettle is a Guardian columnist