Hartwig Fischer, who took over the directorship of the British Museum from Neil MacGregor two years ago, has no decoration on the plain blue walls of his office. There are glass-fronted bookshelves. There ia a desk and chairs and two enormous sash windows looking out on to the great forecourt. (Or, more immediately, on to what some staff call the “Bake Off tent” – the ugly temporary structure through which visitors must currently pass for security checks.) But there is nothing to signal Fischer’s taste – nothing like the glimmering wall sculpture by El Anatsui that MacGregor had; nothing like the array of Staffordshire pottery that Tristram Hunt displays in his office at the V&A; no equivalent to the Paula Rego that Maria Balshaw favours in her lair at Tate. There is only a reproduction of a Cycladic figure on the fireplace, a leftover from the MacGregor years, and, on his desk lamp, a tiny figurine of Sai Baba, a spiritual master revered as a saint, which Indian friends gave him.

Instead, he says, he prefers to concentrate on the people who come through his doors – and the great treasure house of the museum. But the blankness of his working space radiates through his personal manner: he is warm and friendly, but oddly remote. His employees contrast the charismatic immediacy of MacGregor, who had the disconcerting habit of plonking himself down by random staffers in the canteen and interrogating them about their work, with this more distant figure, who speaks softly and carefully, who glides modestly around the galleries, who is sphinx-like in his statements. But for all that, he is quietly formidable, and has vast ambitions for the museum – plans that will, if they see the light of day, transform the museum for generations to come.

Fischer, 56, who came to London after running the state museums in Dresden, is aiming to put the museum, in all its shopworn grandeur, through a major renovation project that will culminate in a complete redisplay of its galleries. That doesn’t sound so remarkable until you begin to absorb the scale of the job. When I joke that it can’t be as big as the Palace of Westminster’s renovation, which will cost at least £3.5bn, he tells me that the museum has more rooms than parliament – 3,000 versus 1,100 – and that the state of the essential services, such as electricity, gas and water are in dire need of repair, just as they are at Westminster. He has in mind something as grand and decisive as the “projet grand” Louvre, which saw the building of IM Pei’s dramatic pyramids and cost between F6bn and F7bn (around £780m at 1993 prices). Or the recent renovation of the Rijksmuseum in Amsterdam, which saw the institution closed for a decade and a bill of €375m.

The museum is set for a multi-million pound renovation under Fischer’s directorship. Photograph: John Walton/PA

Unlike Amsterdam, though, Fischer says: “We cannot close the museum. It’s entirely out of the question.” The British Museum is the most visited attraction in Britain, with 5.9m visitors last year. Work will have to be phased. It will take years. As for even a vague price tag, he is not to be drawn: assessments are still being carried out. And who will pay? Clearly, there will have to be the mother of all fundraising campaigns. But Fischer carefully notes that the Louvre and the Rijksmuseum were renewed “with the support of their governments”. What Fischer hopes to achieve by the end of all this is a display that is more coherent – and more interconnected. That means reshuffling the Egyptian, Greek and Roman collections so that they are not scattered between two floors as they are at present, and also finding ways to show that, as Fischer puts it, “human history was driven and has always been driven by exchange, by cultures communicating”. The interconnectedness he is keen to demonstrate might also be across time: towards the end of our interview we go over to the museum’s big exhibition space, where a stunning show on Rodin and ancient Greek sculpture is being installed. It’s the first exhibition to have been largely developed under his leadership, and its approach – looking at how an artist was shaped by his understanding of the past – might prove a hint at the shape of the programme to come.

It’s an intriguing time to be considering the renewal of the British Museum – one of the world’s few so-called “encyclopedic museums” – as Fischer puts it, “a museum of the world for the world”. But Britain is on the brink of Brexit, turning its face away from Europe. When I ask Fischer if he would have taken the job had it been offered on 24 June 2016, he says: “Yes, without any hesitation whatsoever.” This contrasts to the view taken by the late Martin Roth, his predecessor at Dresden, whose resignation from the V&A in September 2016 was said to have been hastened by disillusion at the referendum.

The museum’s job, Fischer says, is to take the long view, to confront the whole of human history, to understand that Brexit is a moment in the turbulent story of the world. But at the same time: “Everyone who knows me knows I come from a European background and that Europe, as it developed after the catastrophe of the wars is something very important and precious to me. The museum has a lot to offer to help people to contemplate and reflect on what the right decisions should be without taking a direct political stance. It’s there as a space to think, reflect, debate.” It is true that Fischer could hardly be more European. He was raised in Hamburg, studied in Italy and France, and has worked in Switzerland as well as Germany; his wife is a psychotherapist in Paris. It’s easy to imagine what his personal views might be, even if for now, they are cloaked in civil service neutrality. He simply says: “Whoever comes in here and crosses the threshold is not a foreigner. There are no foreigners here. This is a world country, this museum. While at the same time we recognise that this is a British creation, to which the cultures of all the world have contributed.”

Part of the Parthenon sculptures, which have long been the subject of a reclamation dispute between Greece and Britain. Photograph: Graham Barclay/BLOOMBERG NEWS

Contributed, yes – but not always willingly. The museum’s collection is inextricably entwined with Britain’s dark imperial past. Increasingly, nations want their objects back: not just the Greeks and the Parthenon sculptures, but others – there is a longstanding claim from Ethiopia, for example, about works of art plundered from Maqdala after its capture by the British in 1868.

Fischer’s answer to this is that the museum will bring a much greater sense of self-scrutiny to its displays. “The museum has to be completely open about this – that’s the first duty,” he says. “Take the history of the Rosetta stone [the trilingual inscription dating from 196BC that led to the deciphering of hieroglyphs]. In a nutshell, you have the whole intricate layering of curiosity, quest for knowledge, understanding, discovery and possession. At the same time, it’s the ‘Great Game’, the story of colonial and imperialist outreach and imperial conflict. And it led to the deciphering of a language that was hitherto inaccessible, and the understanding of Egyptian culture.”

It’s all very well, I suggest, talking of the museum as an international project, and even as a space where international co-operation between colleagues can continue when formal diplomatic ties are strained. (Fischer made a visit to Iran in December; when we meet, he has just returned from Egypt.) But the buck stops for many with the objects themselves, with the fact of possession and ownership. “When you go to see the Parthenon sculptures,” he says, “you can read about the different views, the conflicting views, and we respect different views.” Respecting views is one thing, but keeping the objects is another – that’s the line drawn right there, isn’t it? “It is a line. But what’s been created here is a major contribution to humanity. So while I respect these views, I always say what has been created here, which is open to everybody, creates an extraordinary opportunity to see cultural heritage in a context you have in only a very few places. That is the museum’s major value and it is very precious.”

Despite the museum’s status as a symbol of Britain and a repository of global knowledge, it is under huge pressure. Its funding from central government has stayed flat during the past decade; in real terms, a 35% cut. Forty-four jobs in research, conservation or curatorship have been lost between 2006 and 2017. Fischer says that the cuts have been in proportion, and curators are no worse off than other parts of the organisation. The picture is, in fact, more complex. There has been a sharp rise in agency jobs in the public access and events departments. And overall, the fundraising department has grown – a sign of the changing times and priorities. Meantime, 60 facilities management staff, who had been outsourced to the collapsed firm Carillion five years ago, have been demonstrating outside the museum, demanding to be taken back inhouse. On this, he offers the blandest piece of director-speak one can imagine: “For the time being, we have the arrangement we have, which grew out of a long thinking process, and this is where we are now.” So you’re not going to employ them directly? He doesn’t answer, but his body language says “no”.

Fischer has come into this environment from the relatively easier circumstances of Germany, where government support for culture, though under recent pressure, is understood as a given, not fought over tooth and nail every step of the way. One of the things he is really passionate about is a music festival he has organised; it will see everything from Ligeti and Nono to Japanese temple music performed in the museum’s galleries. “I’ve always worked with musicians in museums,” he says. “When you look at things listening, you look at things differently. The ears make you see more, and the eyes make you hear more.” Ironically, the festival, which is organised in partnership with the Dresden museums, is being paid for by the German foreign ministry. Still, what impresses him in London, he says, is his staff’s passionate sense of public mission. “You would never think about doing something in this place before asking who it is for. You would never get lost in an intricate scholarly debate without coming back to that question: ‘How is our public going to profit from this?’ And I cherish every day working in this environment.”

The music festival Europe and the World: a Symphony of Cultures, runs from 16 to 29 April. Rodin and the art of Ancient Greece runs from 26 April to 29 July.