Long before we actually went there, “abroad” sounded amazing. Admittedly the idea of it filtered through only in glimpses when I was growing up in Essex in the 1970s.

There were the painful letters we were forced to write to French pen friends acquired from God knows where – bonjour, je m’appelle Gaby, j’ai une soeur et j’aime bien aller à la piscine – and the equally painful responses. There was a heavy cast-iron fondue pot at the back of the dresser, almost never used but a testament to the idea that melted cheese was as exotic as it got. But most of all, there was a handful of black and white photographs of my mother in the 60s, when she spoke good enough French and German to land a secretarial job in Geneva for a while.

There she was in a bowling alley, all beehive hair and black polo neck; or in summer, swimming in the lake. In winter, her colleagues reportedly went skiing at weekends, which sounded unfeasibly glamorous. There was even the suspicion of a cigarette in some of the pictures, although we had never seen her smoke at home. Abroad, which she had apparently discovered just by answering an ad on the London underground, was evidently somewhere rules could be broken. It’s no accident that I went for foreign languages at school.

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Remainers are often not that comfortable talking about our identities as Europeans, but that doesn’t mean we don’t have them or feel them intensely at times like this. And when I think about what it means to me to be European, as well as profoundly English, I inevitably end up not with the EU flag or the day-to-day business of the Brussels institutions (touching as it was of Ursula von der Leyen to quote George Eliot on love as we were leaving), but a gut sense acquired in childhood that foreign isn’t frightening, and lives opened up to the world will be more exciting than ones shut away from it.

People who backed remain made and lost their case on more practical, hard-boiled economic arguments, steering clear of this muddier emotional territory. But as Britain reaches tonight’s point of no return from Brexit, it’s the deeper gut feelings that are bubbling up. The battle to stay in the EU was finally lost in December, but the debate about how we can stay European – how to keep the door open, preserve the social and cultural ties that bind, prevent Britain becoming a crabby and shrivelled country alienated from its own continent – needs blowing wide open.

As Brexiters never tire of saying, they only wanted to leave an institution, not a continent, so this should be something they too can get behind. In a typically graceless valedictory rant to the European parliament, seemingly delivered for the benefit of an audience watching at home on YouTube, even Nigel Farage declared that Britons can hate the European Union but still love Europe. People will still drink French wine or lie on Spanish beaches, and some will still work abroad, if quite not so straightforwardly as before (neither Switzerland nor the UK were in the common market when my mum flew off to the mysteries of abroad).

Play Video 2:19 MEPs sing Auld Lang Syne after approving Brexit deal – video

But it’s going to take more than a commemorative 50p coin with some platitudes engraved on it to make a reality of Boris Johnson’s warm words about an ongoing post-Brexit friendship with Europe. For years Britain has hovered grudgingly on the fringes of the EU, present but not quite involved, like a spouse who long ago fell out of love but secretly likes the security of being married.

Well, we’re on our own now, and a new relationship won’t make itself. The only consolation, on a bleak day for anyone who got unexpectedly weepy watching MEPs link arms and sing Auld Lang Syne to their departing British colleagues, is that this is one of the lamentably few aspects of Brexit over which ordinary citizens still have some control. The trade deal that may eventually be done, and the economic consequences I fear will flow from it, are out of our hands now. But remainer or leaver, each of us still has a personal choice to make about how close we stay culturally and emotionally to the neighbours who cannot help but feel rejected.

However much government drags its feet, we are all free as citizens to choose how we treat the 3 million-plus EU citizens still living in Britain, who cross our paths every day as friends, neighbours and colleagues, and have been made to feel gratuitously unwelcome. But it’s also entirely up to us whether we resolve to learn or brush up on European languages, follow European voices on social media, keep up with European novels, films and exhibitions, or occasionally pick up the European newspapers (in English-language editions if necessary) to see how we look from the other side of the Channel.

There is no going back, in a digital age, to enforced pen friends and town-twinning association meetings in dusty town halls. But I wouldn’t be surprised if a new appetite emerges for grassroots groups too, bringing European expats and their British-born neighbours together (I’d rather public money and effort went on that than commemorative coins or getting Big Ben bonging again).

And it’s up to every parent in the country as to whether they raise their children to think of abroad as a threat, or whether they positively encourage wide horizons and the thrill of the unfamiliar. You can take a country out of Europe, if you want to badly enough. But it’s a hell of a lot harder to take Europe out of a country.

• Gaby Hinsliff is a Guardian columnist