Winstone, who also played Dame Barbara in the drama Babs about her earlier life and career, said she had loved getting to grips with the well-known Albert Square character for the flashback episode which will look at the Mitchells in the 70s and explore what made Peggy the woman she was.
Asked what she thought Dame Barbara would have made of her casting, Winstone said: "Well, I think she would love it. She was always very funny when we worked together and I obviously had to have such a deep connection with her and I had the ultimate respect for her.
"There were moments when we were shooting (this episode) where I just I felt her presence and I just felt guided by her. I hope she would love it and I hope I've done her justice.
"And this time because this is a Peggy that the audience also aren't aware of, there were elements of it that I really had to make myself, as well. I felt her going, 'You've got this'."
Kidulthood and Dead Set star Winstone, 37, had previously starred in the 2017 biopic Babs to mark the actor's 80th birthday, with Samantha Spiro also taking on the role to portray a different period of her life, as well as Dame Barbara herself appearing in it.
Winstone said: "It was a real honour to be asked to step into Barbara’s shoes again. I really felt like my journey with Barbara hadn’t really finished and this was a real opportunity for me to book end my journey with her.
"When we shot Babs I got to work with her very closely and became great friends with her. Being asked to step into Peggy Mitchell’s shoes, it’s the one character I didn’t get to do with Babs, so it really felt like such an honour."
Dame Barbara, who was diagnosed with Alzheimer's disease in her final years, died in December 2020 aged 83.
Peggy Mitchell was written out of EastEnders in 2016 when the character was killed off, marking Dame Barbara's retirement from more than 20 years with the soap.
The EastEnders flashback episode will air on Monday at 7.30pm on BBC One.
Watch: EastEnders Soap Scoop! Mitchells flashback episode