Prince William, who had been due to attend and make a speech in his role as president of Britain's film academy, was absent following the death of his grandfather.
The ceremony opened with a tribute to Philip. Hosts Dermot O'Leary and Edith Bowman started the ceremony with a touching tribute to Prince Philip, acknowledging his "very special place in BAFTA history" after he served as the first president from 1959 to 1965.
Prince Philip died at the age of 99 on Friday and his patronage of the BAFTAs meant that his loss was felt deeply by the British film industry.
O'Leary started the tribute, saying: "Before we start tonight we want to say that on behalf of BAFTA, we are extremely saddened by the passing of his royal highness Prince Philip, Duke of Edinburgh, on Friday.
"The duke was BAFTA's very first president over 60 years ago and was the first royal patron, a line that goes all the way through to BAFTA's current president, his grandson the Duke of Cambridge."
Bowman continued: "It was Prince Philip and her Majesty the Queen's support throughout these years that in many ways allowed BAFTA, a leading charity in the arts, to continue in difficult times and to be here today in 2021.
"The Duke of Edinburgh occupies a very special place in BAFTA history and he will be missed. Our thoughts are with the royal family."
How the remote BATFAs unfolded
Presenters including Hugh Grant, Tom Hiddleston, Gugu Mbatha-Raw and Priyanka Chopra Jonas announced the winners from the stage of London's Royal Albert Hall, but recipients accepted their honours remotely, and there was no black-tie audience to cheer them on.
Director Remi Weekes, who won the British debut prize for his first feature, His House, noted the surreal sensation of accepting the award while sitting in his living room in a tuxedo.
The big winner of the night, Nomadland, stars McDormand as a middle-aged woman who travels the American West while living out of her van and picking up short-term work.
Winning director Zhao, who lived among real American travelers for the film, thanked "the nomadic community who so generously welcomed us into their lives".
"How we treat our elders says a lot about who we are as a society, and we need to do better," she said.
The only previous female directing winner was Kathryn Bigelow in 2010 for The Hurt Locker.
The British film academy expanded its voting membership and shook up its rules last year in an attempt to address a glaring lack of diversity in the nominations. In 2020, no women were nominated as best director for a seventh consecutive year, and all 20 nominees in the lead and supporting performer categories were white.
Under new rules that, among other things, made watching all longlisted films compulsory for academy voters, this year's slate of acting nominees was strikingly more diverse, and four of the six filmmakers nominated for best director were women: Zhao, Sarah Gavron (Rocks), Shannon Murphy (Babyteeth) and Jasmila Zbanic (Quo Vadis, Aida?).
Asked what her directing prize meant for Asian women in film, Zhao said: "If this means more people like me get to live their dreams, then I feel very grateful."
BAFTA chief executive Amanda Berry said the academy was "determined to make change".
"We are not there yet, this is definitely still a work in progress, but I am really pleased with how far we have come," she said.
Kaluuya was named best supporting actor for playing Black Panther leader Fred Hampton in Judas and the Black Messiah.
Bakray, 19, won the Rising Star award, whose previous winners include Kaluuya, Kristin Stewart, Tom Hardy and John Boyega.
"I don't know how to feel," she said. "When we filmed Rocks, I thought 100 people would watch this film, max."
Danish director Thomas Vinterberg's Another Round was named best film not in the English language. Vinterberg paid tribute to his daughter Ida, who had been due to appear in the film and died in a car crash at the start of the shoot.
"We made this movie for her, so the honour granted by you, BAFTA voters, means more to us than you could ever imagine," he said.
BAFTAs in craft and backstage categories were handed out in a separate ceremony on Saturday, when Ma Rainey's Black Bottom won two prizes, for costume design and hair and makeup.
Other double winners included The Father (best actor and adapted screenplay), Sound of Metal (editing and sound), Promising Young Woman (British film and original screenplay) and Soul (animated film and musical score).
Director Ang Lee was awarded the academy's top honour, the BAFTA Fellowship.
Actor, writer and director Noel Clarke received the outstanding British contribution to cinema award, dedicating it to "my young Black boys and girls out there that never believed it could happen to them".
