This week, the 81-year-old Kjer, star of 60 films, more than 100 plays and countless radio and television productions, is undertaking a rare visit to London to attend a gala screening of one of her greatest films, Babette's Feast (1987 winner of the Best Foreign Film Oscar), which on Sunday opens a nine-film season of Danish cinema at the National Film Theatre. The Nineties have borne witness to a resurgence in Denmark's cinematic fortunes, a success for which Gabriel Axel's wry fable arguably laid the groundwork. Lars von Trier's Breaking the Waves earned Denmark a further Oscar nomination and the soporific film-maker's inspired hospital drama for Danish television won itself that rare accolade, an international cinematic release as The Kingdom and The Kingdom II.
In recognition of the seminal role of Babette's Feast in the Danish film renaissance, Kjer will recite part of her own interpretation of the Karen Blixen novella from which Axel adapted his film. Kjer, part Simone Signoret, part Katherine Hepburn, is nevertheless playing down her role as the Grand Old Dame of Danish cinema. "I will only be reading part of my interpretation of Babette's Feast, otherwise it would take all night! The whole thing is more than two hours in length, almost as long as the film."
At a time when most actresses of her age are in their dotage, Kjer is headlining in television, booked for more stagework and would love to do another film. Since 1995 alone, she has played Hermann Broch's gruelling Celine on stage and, until last year, she was touring with AR Gurney's Love Letters. Her co-star in Gurney's two-hander was her husband and longtime acting partner Ebbe Rode, who died two months ago, aged 87.
"I wonder why I've continued to work for so long," she laughs. "Maybe it's because I am very shy and when I work I am not shy.
"Next year, for the 250th anniversary of the Royal Theatre [in Copenhagen], I am working on stage in a Karen Blixen story. I will play a witch."
The Royal Theatre has a personal significance for Kjer, too: she made her stage debut there in 1937. Theatrical success came quickly, with a variety of roles in anything from Shakespeare to A Streetcar Named Desire. Once she had overcome a shaky start in film - her first review read "lifeless, bereft of sex appeal, cool and almost trivial" - she was carrying films by the mid 1940s. Again, she thrived on her versatility, throwing herself into comedy - My Wife Is Innocent - and Denmark's attempt at a Hollywood musical, Meet Me in Cassiopeia. Kjer also took roles in more typically Scandinavian fare, in particular the wave of social realist cinema initiated by writers like Leif Panduto and Klaus Rifbjerg.
Over the years, she consistently turned down offers to work in Hollywood and abroad, and demurs at comparisons with Greta Garbo. "I have had a wonderful life here in Denmark and it doesn't seem to be over yet," she remarks. "Why change it? Going away was never a priority when the possibilities for me here were so prestigious."
The last time she was in London, it was over 30 years ago to visit friends such as Laurence Olivier, Vivien Leigh, Michael Redgrave, Spencer Tracy, stage designer Oliver Messel and director George Cukor. As for America, from where the phone rang many times with offers of work, she went there only once to spend a few days in New York sightseeing with her second husband, Svend Bergsoe, a businessman.
Kjer has only worked in English very occasionally, most recently in Robert Mitchum's 1995 film, The Sunset Boys, a World War Two drama shot in Norway. "I've never regretted `not exporting' because I always thought you explain yourself best in your own language," she explains (in English).
Kjer has always lived near Copenhagen. At her big white mansion near the sea, 20km out of town, she says life is very quiet. She lives alone with a housekeeper ever since her third husband, set-designer Olaf Nordgren, died. Her two step-daughters from her marriage to Nordgren visit often. She is happy to be there, far away from the city.
So what, if anything, would she have liked to have done?
"I know I would not have liked to have taken up the offers of Hollywood fame in the Forties," she says slowly. "Truly I have absolutely no regrets. Except I would like to have been a great cook and I think it might be too late now."
Bodil Kjer will be reading at the Gala Screening of `Babette's Feast' on Sunday 6th September, National Film Theatre 1, 6.30pm