But Nichol said she quickly realised none of that was true.
“She was not looking for anyone to be scared of her, or in awe of her, she just wanted to be in the gang.”
Nichol said that it was always “glorious” to spend time with Dame Maggie, and said they would spend time between takes playing the word game Bananagrams.
“She was fearsome at that and really competitive, and really good at it,” she said.
“But that’s the way she was, she was in with the crowd, and just very happy to be part of it all.”
Dame Maggie was known for her sharp tongue on screen and off.
But that didn’t spoil her sense of fun, Hytner told BBC News.
“Everyone knows how witty she was, she had an extraordinary quick, super intelligent acerbic wit,” he said.
“But she was fun to be with, even when you were at the receiving end of her acerbic wit, you had to laugh.
“She was so smart, she was also capable of extraordinary sweetness and was a wonderful companion at concerts, ballet and theatre.”
Harry Potter stars have also been remembering how much fun Dame Maggie was on set.
On Saturday, Rupert Grint, who played Ron Weasley in the film series, posted a picture of him awkwardly dancing with Dame Maggie.
“She was so special, always hilarious and always kind,” he wrote.
“I feel incredibly lucky to have shared a set with her and particularly lucky to have shared a dance.”
Of course, it wasn’t all fun and games.
Asked in her BFI interview to reflect on the most tormented thing she ever did, Dame Maggie recalled a time during the filming of Harry Potter, when she was stuck in a trailer in the snow for a week “with that daft hat on my head”.
“And sitting in that trailer day after day and not being used [while waiting for her next scene], that doesn’t make you feel that jolly. That was a horrid thing,” she said.
“But there were other people in the trailer also moaning like Miriam Margolyes. You’re not alone when you moan.”
Margolyes, who also shared the screen with Dame Maggie in Ladies in Lavender, said the actress always had a “glint of mischief”.
“I saw what a kind person she could be as well as absolutely terrifying,” she said.
“I wouldn’t say I was a friend of hers, I was an acolyte, and she allowed me to be so.”
Margolyes, who played Professor Sprout in the wizarding series, recalled a time when she was absent from filming, as she had finished her role on the show.
“[Dame Maggie] said ‘nonsense! If I’m in a scene, I want you there, so come back please’. And she talked to the producer and got me back, so I got a bit more money.”
She admitted that she was at times scared of her. “But you can forgive someone for being the best of the best can’t you, if they’ve got a bit of a temper.”
From small stage to big screen, Dame Maggie’s moving performances always stole the show.
But she was also immensely dedicated. Even in later life, she was known for never turning up on set without memorising her lines perfectly.
“I never saw her on set with a little script, she knew it before she got here,” Lady Carnarvon, who lives in Highclere Castle where Downton Abbey was filmed, told BBC Breakfast.
“She worked so hard, to get up at silly o’ clock… and to wear corsets for hours on end,” she said, adding that she continued working right up to the end of her life.
“I think inside, there was an anxiety to get it right,” Margoyles said. “But she always did.”
Throughout it all, she remained famously private.
She rarely did interviews. And Margolyes notes that Dame Maggie “didn’t like being on chat shows”, despite being good at them.
When she won her first Oscar in 1970, for her performance in The Prime of Miss Jean Brodie, she skipped the awards ceremony.
At the time, she was acting in a play in London. Many other actors would have let the understudy take over for the night, but not Dame Maggie.
She did show up to accept her Special Award Bafta in 1993, but her speech lasted a mere 30 seconds.
“If it’s possible to be in films without taking your clothes off or killing people with machine guns. I seem to have indeed managed,” she said.
It all paints a picture of an actress who found the whole idea of being a star faintly embarrassing, despite having an entire Wikipedia page dedicated to the number of awards she has won.
“She was a very private person,” Lady Carnarvon added.
“I always wanted to respect that and not overstep any boundaries. Which I think she was in that way, just like her character on TV.”
But despite being determined to go under the radar whenever possible, Dame Maggie absolutely made her mark on everyone she met.
Perhaps her old friend, the late actor Kenneth Williams, put it best, in his diary entry about Dame Maggie in December 1962.
“The weather cold and dreary and mediocre audiences made [Dame Maggie’s] departure drab and unexciting. I didn’t say goodbye or anything, ‘cos I’d have cried.
“But that girl has a magic, and a deftness of touch in comedy that makes you really grateful, and she’s capable of a generosity of spirit that is beautiful.
“She’s one of those rare people who make things and places suddenly marvellous, just by being there. She’s adorable.”