One of the bleaker aspects of the dissociative state that has characterised Britain’s relationship with Europe since World War II has been our neglect of Europe the Place, as distinct from Europe the Project. Most of us don’t seem to care any more which leaders are in charge of which government, large or small, across the entire Continent – or what their policies are.

What’s it got to do with us? we say. They all dance to Berlin’s tune – in this case Ode to Joy, composed, appropriately, by a German.

Overall, we take the view that Europe’s leaders are not to be trusted, just as we assume that the idea behind Ever Closer Union right from the start was to extort money from the British treasury. But other than recognising that we must maintain eternal vigilance against trickery, we don’t much care what goes on on the other side of the Channel.

In the immediate post-war era, any indifference we showed was understandable enough. We had been up close and personal with Europe for most of the previous 30 years, and much good it did us.

But during the four decades, and counting, that we have been part of what morphed into the European Union, we stopped almost entirely thinking of our Continent as being what it is, a rich mosaic of states to whose history we are indissolubly bound. Instead, we now view it, at least in political and economic terms, as a featureless expanse, about as welcoming as the Moon. We resent what we see as the EU’s rigid hierarchy – Germany 1st, France 2nd, the rest joint 3rd – in which we figure only as a square peg in a round hole, because it makes us look small, when we know we are really, really big. Besides, they don’t speak English, except when they’re showing off, or serving us in restaurants, or giving us directions, or trying to sell us something, so how are we supposed to know what the Hell is going on?

Ask most people in England these days (outside of the usual suspects) what’s happening in Europe the Place and they’re likely to say, Muslim immigration, Islamic terrorism and fears over Russia. Ask them to be more specific and they’ll say it’s all a conspiracy masterminded by Angela Merkel. But do we really care if Merkel remains Chancellor of Germany or gets slung out by Martin Schultz? Apparently not. Do we give a stuff who becomes President of France? No. Whoever it is is bound to be shifty and no friend of the UK, we say. As for Italy, do they even have leaders? They’re like something out of a comic opera. And Spain? Not content with taking our tourist billions, Spain wants to steal Gibraltar 300 years after we won it fair and square in a card game, or EuroMillions, or whatever.

Maybe if Boris Johnson had invested some time trying to understand the Italian and German positions on Russian involvement in Syria, he wouldn’t have made such a fool of himself at the G7. He thought, after taking his instructions from Rex Tillerson, that he had additional sanctions in the bag. Instead, not for the first time, he ended up with egg on his face.

And why? As a previous Johnson once remarked, ignorance, sheer ignorance.

Alas, our foreign secretary is not alone. If typical voters think about the nations of Europe at all (other than those poor saps in business trying to strike a deal), they think of beaches, city breaks and dirty weekends. Either that or somewhere we might retire to if the price is right and the local health cover beats the NHS.

Contrast this ignorance with what we know about the United States. Yes, America is also a holiday resort. We go in our millions to New York, Disneyland, Orlando and the Everglades. But we also know the name of the President, whom we judge to be either a good or a bad thing for the world. We know (or think we know) the difference between the Democrats and the Republicans. We know there is a Supreme Court. We know the cops shoot young black men and that angry young white men periodically shoot up the schools they went to. We watch their hit tv shows. We love their sitcoms and their dramas. We adore their music, which we think of as ours. We are addicted to their social media. Having fought alongside Americans in any number of conflicts, some of them meaningless, we have learned to take orders as well as casualties while suffering their contempt. In short, we are like two peas in a pod – except that we’re not. For outside of the Royal Family, costume dramas and John Cleese, Americans rarely give us a second’s thought.

Do we offer our one-sided embrace because we used to own them? Partly. But just as likely it’s because we share a language. By the same token, we choose to believe that Australia and New Zealand, with a combined population less than Poland, can somehow take up our economic slack. Know what I’m talking about, mate? Know what I mean? ‘Course you do.

But we can’t go on like this. Are we grown-up or what? Brexit (as I last remarked a couple of days after the Referendum) gives us a unique opportunity to re-set a network of relationships that, starting with the Roman occupation, goes back more than 2,000 years. We in the UK like to think we know a thing or two about history. Well, two-thousand years is a lot of history. But with the weight of Brussels and the EU lifted off our backs, we can begin once more to see Europe for what it is – not an anti-British cartel, but the most remarkable collection of countries on the planet, without whose genius the high-points of human achievement would be the Egypt of the Pharaohs, the bloody rule of the Incas, the art and science of the medieval caliphate and the two hundred years or so of dynamic governance that preceded the long stagnation of Imperial China.

We should not, however, deceive ourselves. At a political level, the scope for change is limited. So long as the EU exists, Britain will be obliged to negotiate trade and standards with the collective, not with its component parts. UK ministers will be forced to spend weeks and months in Brussels each year sat across the table from the same unelected bureaucrats that face them now. We will still have to discuss defence in the context of Nato, and policing and security by way of Interpol and Europol. The backdrop to our dialogue on peace, justice and the explosive movement of peoples will continue to be the United Nations charter and the European Convention on Human Rights, the latter drafted in 1950 by British lawyers and never a part of the hated EU acquis. Most crucially of all, though our borders will be brought back under domestic control, foreigners will still begin at Calais.

But we are where we said we wanted to be, and given that we have walked out of the collective we now have the chance to reacquaint ourselves with its inhabitants, many of whom, it is easy to forget, are old friends as well as neighbours.

Issues will arise. There will be events. Stuff will happen. There will be times when Paris or Berlin (or for that matter, Lisbon, Prague or Warsaw) will be keen to work with London to resolve a problem or confront an issue. The Foreign Office, no longer tied to a communautaireapproach, will be liberated. Outside of the narrow remits of the EU, our diplomats will be able to build links and networks unrestricted by constant reference to the deliberations of the European Council or the line set down by the so-called External Action Service.

But it can’t end there. If it did, leaving would make no sense. Europe should be just the starting point. The Government has to look like it means business on the grand scale – or as grand a scale as a medium-sized power, slightly foxed, can manage in the 21st century. We need a strong conventional military – bigger and better equipped than the one we have today – and in particular an expanded Navy. But we need also to avoid the temptation to further slim down the Foreign Office. It would be a bitter irony if we flounced out of the EU specifically to escape the suffocation of Brussels only to decide that in future we will run our foreign (and defence) policies in lockstep with Washington. Independence has to mean independence, not diplomacy on the cheap. Global has to mean global. And that means a foreign office that is both properly funded and sure of its role.

Early days, of course. The hurdles we face in the Brexit talks will keep us busy on all fronts for the next five years, while negotiating the “brilliant” trade deals we are promised with all and sundry should keep us occupied long after that. We need to take our time and get things right. Only if we are prosperous and well-connected can our ambition to be a global leader move out of the dreamscape into the real world. For our children and grandchildren to be convinced that quitting the European Union was not a disaster, based around short-term issues of immigration and misplaced pride, we have got fundamentally to rewrite the role we play on the international stage so that, as free Europeans from a proud heritage, we come to be viewed not only as entrepreneurs and financial fixers, who make weapons on the side, but as an admired diplomatic consultancy, or global resource, ready to step in anywhere, anytime to help make the world a better place. Trade follows the flag, they say, and the Union flag (assuming we still have a union) must be firmly planted in every one of the world’s capitals.

Brexit must not be used as an excuse to retreat into ourselves. That truly would be an exercise in self-harm. It is a chance to show the world what we’re made of, or it is nothing.