Tiffany Jenkins doesn’t remember seeing the Elgin Marbles as a child. What stood out for her on her early childhood visits to the British Museum were the Assyrian sculptures, the imposing figures of bearded, winged lions from the palace of Nimrud, creations that seemed like “something out of your imagination, dragon-like, with a frightening, magical quality.” Even now the sociologist seems breathless with wonder at the fact they were created in 850 BC. “Being able to get your head round that places you in history a little bit.”

But it is the fate of the Elgin Marbles, and the controversial question of whether they belong here, in the British Museum, or in Greece, that forms the starting point for her book, Keeping Their Marbles: How The Treasures Of The Past Ended Up In Museums… And Why They Should Stay There, an exploration of the debates around repatriation and post-imperialist cultural atonement. Jenkins, as the title suggests, believes they should remain. “They’re very much part of our culture,” she says.

We meet at the Monument on Calton Hill, in Edinburgh's wind and hail, Jenkins impervious to the weather: she’s used to a walk up the hill, living as she does, near Arthur’s Seat, in the flat she shares with her husband, the political commentator and Herald columnist Iain Macwhirter. Nothing in Edinburgh speaks more boldly of the influence of Ancient Greece here in Scotland, than this three-dimensional half-finished sketch in stone mimicking the Parthenon, nicknamed Edinburgh’s Disgrace. It is a reminder of how we live with Ancient Greece in our Athens of the North.

That reminder is there in our banks too, as Jenkins notes. “If you think about all the columns on the buildings of our banks, they really all come from that.” One of her points in the book is that Ancient Greece, in the form of its artefacts, belongs to everyone. Others disagree. They say it belongs to the Greeks.

But this is no dry analytical tome, it actually makes for a cracking tale. It begins with exploration, Captain James Cook's voyages to the Pacific and the natural history specimens and cultural artefacts he brought back, and involves conquest, trade, exchange, colonisation looting, the enlightenment thirst for knowledge. There is Lord Elgin, ambassador to the Ottoman Empire, more hero, perhaps, than villain, saving, or so he thought, those Greek marbles from the Turks, who were using the Parthenon as a quarry. And there is Napoleon, whose conquests and campaigns stocked the Louvre museum with treasures.

Then there is argument and controversy, big ideas, the belief in "knowledge for knowledge's sake". Underlying all of it is the question: Who owns culture? And not only that: who is best placed to be it's guardian and interpreter. It's a timely question. The destruction of many of Palmyra's ancient buildings by Islamic State brings it into sharp focus. “These issues about who owns culture, what we do with our past, how do we react to imperialism,” says Jenkins, “these are things that people feel extremely passionately about.”

Jenkins sets her arguments out unflinchingly, yet with balance – a Wall Street Journal review described the book as "a tough examination". She is not one for holding back from the bear pit of controversy, or saying things that are, in our times of sensitivity and colonial guilt, almost politically incorrect. The idea we should keep the Marbles or that aboriginal people should not have their human remains or other artefacts returned to them, has potential to offend. But she seems happy to bring that on. A former director of the provocative libertarian think tank the Institute of Ideas, she has chaired and debated in many an event, and likes, it seems, in her own elegant and eloquent way, a good ding dong.

For many years now the 42-year-old has lived between London and Edinburgh, the latter being where she writes and has her private life. She feels “an outsider” in both. She relates, in this sense, to her American mother, who was told she seemed British when in America and American when in Britain, and felt was always somewhere else wherever she was.

Originally, she came up while doing events for the Institute of Ideas at the Edinburgh Book Festival. It was at one of these that she and Macwhirter met. They were back then, and now, she observes, “politically poles apart”. “Often we take different sides. He voted Yes in the independence referendum, I voted to stay. We had a string of No Yes No Yes No Yes stickers in the window. Iain went and got me some No stickers, which is a proper sign of love.”

Party politics, for the most part, she says, does not speak to her at all. “There’s very little life in politics, or sense of possibility. It’s very much about being risk averse, not rocking the boat.” She believes “issues that perhaps would have once been thrashed out in the political sphere have gone elsewhere”. Meanwhile, she says, some really important and passionate debates are happening in the cultural world. Her latest project is on secrecy.

The recent story of museums, she says, tells a great deal about our society and its relationship with the past .Since the nineties, she says, we have seen the growth of what she calls “contrition chic”, the desire to atone for past wrongs by giving back the relics of other societies. “We are these days much more backward looking than we were and it’s much more about the victims. Whereas previously Napoleon wanted to associate himself with antiquity because it was all about great leadership, now you have Cameron [saying sorry for the Bloody Sunday massacre and Hillsborough] or Tony Blair [expressing sorrow over the Irish Potato Famine and Britain’s role in the slave trade] apologising for something they had nothing to do with. And it is seen as positive. I don’t think it is. It presents people as vulnerable, unable to take control of their own future. And it kind of makes political leaders look good because they’re the ones that get the moral authority from it.”

For some time she has been troubled by the trend towards repatriation of a whole range of different objects, particularly human remains, which formed the subject of her PhD. One of her concerns is that the impulse to repatriate has often come not from those communities but from within the museum establishment. It has also, she observes, coincided with a shift in politics. “Indigenous movements used to argue for land and for political equality, for equal rights, better living conditions, all good things. And when that didn’t quite happen you see a move away from that towards more cultural recognition and demands for objects and human remains.” Meanwhile, the communities themselves often suffer from deprivation and low life expectancy.

Jenkins, who studied history of art as an undergraduate, has always, from childhood, been a fan of museums. She loved “their other-worldly nature” and “the way you go in grumpy and you come out having been transported to another time and another place”. Growing up in Oxford, she recalls having been taken to the British Museum, but also, more locally, to the Ashmolean and the Pitt Rivers museum of anthropology.

Her father was an academic, a geography lecturer at Oxford Polytechnic, her mother an American who met him when she taught him a course. Jenkins recalls that as a child she was “always a bit of a dreamer, and always had my head in a book”. Still better than books were museums. She vividly recollects the shrunken heads displayed in the Pitt Rivers. “It’s the sort of thing little children terrify themselves with,” she says. “I remember that kind of exhilaration you sometimes get when looking into the oddness of the past. Because you like being frightened.” As she points out, some of the biggest attractions for families, for children, are human remains: mummies and bog bodies.

She worries about what has happened in the last 30 years to museums: their attempts to become more popular and accessible. “Museums tried to repurpose themselves, to move away from things they think aren’t popular.” Often she notes, politicians seem apologetic or defensive about them. “A culture minister would say things like museums are dusty and old, or difficult and elitist. All things that I don’t think are quite true actually. The British Museum has 6.5 million visitors a year.” Meanwhile, institutions like the National Museum of Scotland on Chambers Street, she describes, have now become “like playgrounds”, in which you “don’t necessarily see the objects”.

One of the things that concerns her is the disappearance, both in universities and museums, of the dedication to “knowledge for knowledge’s sake”. “These institutions are now seen as there," she bemoans, "to improve the economy or create a sense of self-esteem, to ease mental health problems. All these things, except for the one thing they can do which is to purse the dissemination of knowledge. I’d like this book to remake the case for what museums can do.”

Jenkins does that. And more. She shows why museums should still very much matter to us today.

Keeping Their Marbles: How The Treasures Of The Past Ended Up In Museums And Why They Should Stay There is published by Oxford University Press,