For her book choice, she also chose Sir Paul’s memoir Japanese Jailbird, written by him but never released.
The manuscript – detailing what happened in 1980 when the star spent nine days in a Japanese jail for a drugs offence – has been locked away for decades with the only copies given to his children, something that Stella said she finds “very beautiful”.
She went on: “I just think it makes me remember family and it would make me also remember freedom.”
The 45-year-old also praised the late David Bowie after choosing his song Starman as one of her tracks.
“What an amazing talent and again so modern, so relevant and so individual. What an incredible, individual voice he had,” she said.
Speaking about Blackbird – on the 1968 album The Beatles – Stella said the track had “never aged”, which she described as shocking.
“I’m really proud of dad that he wrote it at such a young age, he had this sort of incredible vision to understand politics, to understand poetry,” she added.
She recalled how music was a huge influence on her childhood and her father would come home every day from the studio and she would listen to what he had created.
Stella spoke of meeting many famous faces from the music world, such as Quincy Jones and Michael Jackson, who all had “an incredible influence” on her.
The designer told the programme she often used the name Stella Martin while at school and studying at London’s Central Saint Martins college to avoid being recognised.
Her final year show in college hit the headlines after famous faces such as Kate Moss, Naomi Campbell and Yasmin Le Bon wore her designs on the catwalk.
“I look back on that moment and just feel a bit embarrassed that I was so naive,” she said.
The designer went on to defend some of the expensive price tags on items in her fashion range.
When asked about the “ethics” and “morals” of someone paying thousands for a dress, she said: “Look at some of my competitors and that’s probably fairly well-priced.
“I mean, I do struggle with that concept, but I work really hard to have a lot of products that are available on a better price point.”
Stella McCartney’s full Desert Island Disc track choices were:
Smells Like Teen Spirit by Nirvana
Road to Nowhere by Talking Heads
Blackbird by The Beatles
Starman by David Bowie
Something by Phyllis Dillon (a reggae version of the George Harrison-penned Beatles song)