Sigrid Rausing, 62, is a publisher and former editor of Granta magazine. When her best friend, the acclaimed Swedish writer Johanna Ekström, became terminally ill with cancer, Rausing promised to complete her last book. She edited the 13 handwritten notebooks, adding her own commentary. And the Walls Became the World All Around (Granta), which Rausing has now translated into English, is a brave and beautiful memoir of Ekström’s final two years, and a moving meditation on grief and friendship. It was a bestseller in Sweden, where it was first published last year. Ekström died in 2022, aged 51.

Did you have any reservations about agreeing to finish Ekström’s work?
I was in Stockholm helping to look after Johanna in the last few weeks of her life, and I didn’t know she was working on this book. She told me about the notebooks and asked me to finish it – and of course I said yes. These promises, they are not like anything else. They are like a vow. A binding obligation.

How did the book evolve?
What started out as a writer’s notebook gradually turned into a text on loss: first of all, of an important relationship – Johanna was very much in love with a man who had entered into deep depression – [then] her elderly mother was dying, and it was the pandemic. She also noted the first signs of her illness, visual disturbances and physical symptoms she thought of as psychosomatic.

Ekström died of an eye melanoma. One poignant, almost prophetic, aspect of the notebooks is the number of visual metaphors, even before her diagnosis.
Yes. A lot of her writing, even before this book, evoked seeing as a metaphor, partly because she had unusually good eyesight, a visual clarity and memory most people don’t have.

The title is a line from the classic children’s book Where the Wild Things Are by Maurice Sendak, when the little  boy, Max, is confined to his room – his imagination transforms it into a jungle. Ekström, similarly, began writing during the pandemic…
The book is very much in the tradition of Covid writing and that sense in which the home became the stage for intimate details; writers paying close attention to what they could see and hear.

And the Walls… is, above all, a grief memoir. Was working on it consoling as well as painful?
To have the discipline of working while I was really grieving, to be able to stay with Johanna’s voice for that long, was wonderful and, yes, consoling.

What was Ekström’s background?
She was very much in, and of, the Stockholm cultural sphere. Her mother was a writer. Her father was a writer and an editor, the head of Swedish PEN and eventually the head of the Swedish Nobel committee for literature. That was the environment she grew up in and, to a great degree, remained in.

She published 13 books in different genres. Yet this is the first to be translated into English. Why do you think this was?
She started out as a poet with a debut collection when she was just 20. But she is most famous for her memoirs of growing up in that environment: Om man håller sig I solen (2012) and Meningarna (2020), which roughly translate as “If You Stay in the Sun” and “The Sentences”. The first one is a brilliant account of quite a troubled childhood, and the second is a book-length essay about her mother. The only reason they haven’t been translated is because they are so culturally specific, whereas this book, which addresses broader questions of illness and loss, is much more universal.

Despite the humour and joyfulness, the notebooks are also full of sadness, even before the diagnosis. Ekström spent many years in therapy and writes of feelings of hopelessness. Was this always something she struggled with?
I think those feelings of desolation that she writes about in these notebooks had always been with her, but they haven’t always been part of her writing. They didn’t have much to do with her illness, which she faced with great resolution. She was both extremely imaginative and absolutely realistic. So she was bleakly realistic about her illness.

How did you feel when you finished the book?
It felt very blank. When you’re working on a text there’s always a sense of loss when it’s done. But finishing the translation of a book by my best friend who had just died brought a much greater sense of loss, because I was no longer with her. She is gone now.

What are your views on the proposed assisted dying bill?
I’m wholly in favour of a change in the law on the grounds of self-determination, the right to make decisions about our own bodies. I find it abhorrent that the state should make those decisions for us. This is a right that I want for myself.

What was it like working in your native Swedish?
It was interesting. Swedish is much more precise than English. It’s also almost impossible to translate yourself. But it was very compelling to submit myself to somebody else’s voice in such a disciplined way.

Last year you stepped down as editor of Granta magazine after 10 years. What next?
I’m the publisher of the magazine, so I’m still very much involved – and of course I’m the publisher of Granta Books. I’m also working on a book about my husband, Eric Abraham, who was a young journalist in apartheid South Africa, who was placed under house arrest and banned, and eventually escaped to Britain. The book is about family, trauma and history. And we’ve started a new imprint, publishing books that emerge from  Granta magazine pieces. I’ve just finished editing a translation by the German writer Judith Hermann – we published a fascinating extract from the book in the magazine, about an accidental meeting with her psychoanalyst late at night.

What are you reading at the moment?
Essays by the American literary critic Edmund Wilson. Nobody talks about him any more, but what a good essayist and travel writer he was.

• And the Walls Became the World All Around by Johanna Ekström and Sigrid Rausing is published by Granta (£16.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply