The Harry Potter actress, 76, uttered the F-word in January while regaling an anecdote involving Hollywood star Warren Beatty.
ITV apologised and said that Margolyes had been briefed about offensive language beforehand.
Watchdog Ofcom launched an investigation but has now said it considers the matter “resolved”.
The veteran actress had asked Peston: “I’m going to use a bad word now. Can I use that in the morning on a Sunday?” and the presenter replied: “Yes, yes, it’s you.”
Referring to a meeting with Beatty on the set of the 1981 film Reds, she said: “So I knocked at the door – in the lunch hour – and he said ‘come in’, opened the door, he looked me up, down, up, and said, ‘do you f***?’”
ITV said it “did not think that the word she intended to use would be f***”, while Ofcom accepted that Peston “was clearly unaware what the ‘bad word’ would be”.
An Ofcom spokeswoman said: “We found offensive language was used in this programme before the watershed.
“We took into account that the word ‘f***’ was used in a live interview and that the production team had briefed Miriam Margolyes before going on air and had reminded her that it was a live show.
— Peston on Sunday (@pestononsunday) January 14, 2018
“Robert Peston accepted responsibility and apologised for the language immediately after the interview and before the end of the programme.”
The swearword left the studio guests – Tory MP Sarah Wollaston and Lord Adonis – giggling, while Peston was forced to apologise.
And he quipped “and you’ve just got me sacked, which was a public service”.
Margolyes appeared to put her hand over her mouth in surprise following the apology.