Anthony Minghella's final film had a "bitter-sweet" premiere on Tuesday night, hours after it was announced that the revered director had died.
Minghella won a number of awards including the Oscar for best director
Alexander McCall Smith, who wrote The No 1 Ladies' Detective Agency, said the "very moving" London event went ahead on the wishes of Minghella's family.
The film is due to be shown on BBC One on Easter Sunday.
Colleagues of the film-maker, who died aged 54 after suffering a haemorrhage, have continued to pay tribute.
His US agent, Leslee Dart, said he had the haemorrhage days after he had surgery for cancer of the tonsils and neck.
He died at about 0500 GMT on Tuesday at the Charing Cross Hospital in Hammersmith, west London.
Minghella co-wrote the screenplay for The No 1 Ladies' Detective Agency, based on McCall Smith's novel, along with Four Weddings writer Richard Curtis. The film was shot in Botswana.
McCall Smith told BBC News: "It was a bitter-sweet occasion last night.
"It was very, very moving and made all the more moving by the sad circumstances - but what a beautiful film he's made.
"The remarkable thing is that Minghella didn't really have great experience of Africa before he did this.
"He went there and he understood, he really understood."
Detective Agency actor Lucian Msamati added: "I had a lot of fun. To be part of something so wonderful and to have the privilege of bringing Alexander's lovely characters to life is a true honour."
A TV series featuring the same cast, including singer and actress Jill Scott, is due to be filmed in the summer.
Labour MP Sir Gerald Kaufman has tabled a Commons motion mourning the "sudden and untimely death" of "a charming and genial human being".
His tribute follows a number made by stars and colleagues following Minghella's death on Tuesday morning.
Jude Law, who worked with Minghella on three films, said: "He was a brilliantly talented writer and director who wrote dialogue that was a joy to speak and then put it on to the screen in a way that always looked effortless."
And UK Prime Minister Gordon Brown, directed by Minghella in a Labour Party broadcast before the 2005 General Election, said: "He was one of Britain's greatest creative talents, one of our finest screen writers and directors, a great champion of the British film industry and expert on literature and opera."
Minghella began his career as a writer of radio plays before he made his debut as a film director with 1991's Truly, Madly, Deeply.
He went on to write and direct film versions of Michael Ondaatje's The English Patient - for which he won the best director Oscar in 1997 - and Patricia Highsmith's The Talented Mr Ripley.
He also directed 2003's Cold Mountain, starring Law and Nicole Kidman.
And in 2005, he directed his first opera, an English National Opera (ENO) production of Madama Butterfly.