If, like our King, you have the misfortune to be diagnosed with cancer, then you may find help and support at a Maggie’s Centre, named after the late writer and garden designer Margaret Keswick, who died in 1995.

As the King had tests in hospital, the Queen was opening the most recent branch, in the grounds of the Royal Free Hospital in Hampstead, north London. Like the other 24 around the UK, it provides restful, quiet spaces where people can come and sit, think and read, get advice on health and funding, or simply help themselves to coffee and tea in the ground-floor kitchen area —the focal point of all the Maggie’s Centres.

Each centre is designed by an architect whom Keswick and her late husband, the architectural critic Charles Jencks, admired for their creativity and independence. The centre at the Royal Free was designed by the Jewish Polish-American architect Daniel Libeskind, who argues that in life, as in architecture, there are many more outcomes—and many happier outcomes — than those that fate seems to prescribe for us. For some people with cancer, that’s a promise that may hold out false hope but it’s more welcome than the opposite.

After he flew into London from New York last week to meet the Queen at the opening ceremony, he told me that architecture has to confound what we take to be reality, in the same way that we have to challenge the apparent inevitability of cancer. “We have a very limited idea of what architecture really is. We think of it as a consumer item, like buying a refrigerator or a car, but architecture is not like that at all.”

Libeskind’s idea that a building can spring, like hope, from the soil of affliction is a message that anyone devastated by cancer will clutch at. By contrast, when Margaret Keswick was told at the Western General Hospital in Edinburgh in 1993 that her cancer had returned and was incurable, she and her husband were left to process the news in a windowless corridor.

It was that experience that inspired her to start the “Maggie’s” project. She was determined that people should not “lose the joy of living in the fear of dying”. The day before she died, in July 1995, she sat in her garden, face to the sun, and said to her husband: “Aren’t we lucky?” What Libeskind has brought to the growing collection of Maggie’s Centres, some of them abroad, is an architecture which embraces that idea of an alternative reality — an architecture of optimism.

Libeskind’s architectural animation offers spiritual refreshment. For all the good work that the Royal Free does, it is a physically dispiriting 1970s building, with all the most dire characteristics, externally and internally, of the NHS at its architecturally most oppressive. The new building, shoehorned onto a tiny patch of land at the back of the older building, challenges the 12-storey concrete-and-glass grey block that looms over it by suggesting that all is not lost and that life has the power to break through and surprise.

It does this by symbolically rejecting what everyone accepts without question: the assumption that buildings have to be defined by convention — that they have to be rectangular and static. Libeskind shows instead that buildings can be plant-like and alive, with curving walls that widen and curl as they rise out of the ground — in this case like brassicas (of the genus cruciferae—a neat comment on the tower of the 1970s Royal Free buillding which is cruciform).

Libeskind has been designing buildings that offer alternative realities ever since setting up his practice in 1989. What is intriguing is to see how the meaning of those alternatives has changed. In his earlier years as an architecture teacher, in London and elsewhere, his radically abstract designs had seemed capable of existing only on a sheet of paper.

Then, he found a way of giving his collisions of lines and angles physical form, in the various Jewish museums and Holocaust memorials that he has become famous for, with massive zigzaggy leaning walls acting as metaphors for the violence and cruelty inflicted on Jewish communities by Nazi aggression.

Today, with computer simulation now a standard tool of architectural representation, complex geometry is no longer difficult to conceptualise or to build, and what had once been the last word in in avantgardism can offer the benign aspects required of a centre for solace.

On the face of it, the idiosyncrasy of Libeskind’s architecture seems to detach it from normality, marking it out as affordable only to the very wealthy, who like to treat the unusual as a sign of their superior taste. Barratt Homes don’t build housing estates like this, after all, because curvy sloping walls (what Libeskind’s project architect calls “non-rational curvature”) can only add hugely to the cost.

Not so, Libeskind tells me. Unusual forms can solve problems more efficiently than standard solutions. “We think that the right-angle is the cheapest angle but it’s not true. It’s a mythology. Sometimes the right-angle is much more expensive than a wall at a 30-degree angle.”

Is the oddity of Libeskind’s buildings the product of his own dislocation? He is the son of Polish-Jewish Holocaust-survivors who moved to New York City (after two years in Israel) when he was 13, and who spoke Polish, Yiddish, Hebrew and Russian —but not English — when they set up home in the Bronx in 1959. That surely gave him so little investment in American mainstream culture that he was left to make up his own rules, in architecture as in other things, as outsiders often do.

Again, no. He came to think of himself as an American “the moment I stepped off the boat. We stepped off the boat, my sister and I, and we felt we were Americans. Instantly. I don’t know how. There was no transition.” Because they had moved into a Jewish area? “That’s certainly part of it, because the neighbourhood was full of survivors of the Holocaust but when I went to school, I was with Irish, Italians — the classic Bronx mix. It was the diversity of New York that made us feel Americans right away.”

Would it have been different if the family had settled elsewhere—in the rural communities in the west and south that Philip Roth wrote about in The Plot Against America as places for Jewish boys to be sent to be stripped of their racial identity? “I have no idea.

“My first job as a professor of architecture was at the University of Kentucky in Lexington, which is really the Midwest, but it was the same. I didn’t feel it was only New York that provided a refuge for freedom. And people were so nice everywhere.”

Marriage to Nina Lewis in 1969 only rooted Libeskind more deeply. His own parents became factory workers, his father as a printer, his mother in the garment trade.

Her father, although also arriving as a Yiddish-speaking immigrant, was a Canadian labour lawyer, a Canadian MP and leader of the New Democratic Party, which he’d helped to found. Her brother Stephen led the same party in Ontario, making the Lewises one of North America’s great political dynasties, like the Trudeaus. Time magazine ran a cover story about them as the Kennedys of Canada. But Jewish, not Catholic.

After getting married, Nina worked in public advocacy around the world, at one time heading the Citizens Advice Bureau in London. In 1989, when Libeskind won the competition to design the Jewish Museum in Berlin, he started his first studio and invited her to join him. “She said, ‘How can I work with you? I’ve never been in an architect’s office.’

“And I said, ‘The same applies to me.’ I worked for one or two days for an architect but I rejected it: it was too boring. So we both started our practice without knowing what an architect does.”

Was it her job to suppress the mad ideas and introduce reality? “On the contrary!

“She is the one who makes things possible. I also work with other fantastic people in our studio in New York, so I have a lot of help, but she is a true partner creatively — because she always says ‘Yes’.

“For example, we are working on an unprecedented Unesco project in Auschwitz called Barrack Seventeen. For the first time in 15years, the six former countries of Yugoslavia have agreed to work together, because of what we’re doing.

“That’s Nina! She accepted a call from a stranger who was interested in sponsoring a permanent exhibition about the former Yugoslavia’s experience of the Holocaust, and everyone in the office said ‘Are you crazy?’ but that’s who she is. She’s got positivity to a degree that I know in no one else.

“Her role is one of great insight. When I first started working with her, I showed her a drawing that I was very proud of and she said ‘What’s so great about this?’ and I suddenly realised, all my life, I’m just talking to other architects. I wouldn’t call this realism: realism is people who’ve given up on imagination.

“But she’s got a great imagination and she’s the one who dares to do what architects don’t dare to do. If she said tomorrow that she was changing career, I’d close down.”