The article by political editor Isabel Oakeshott, called "Labour big beasts maul Ed Miliband", quoted Prescott as having told "friends" that "it is only early days, but it has not been a great start" by Miliband.
Prescott then tweeted: "I see there's a quote purporting to be from me in the Sunday Times. It's completely made up. An absolute lie."
He went on to claim that Oakeshott had called his ex-directory home telephone number looking for a quote for the article and he told her "never to call the number again and put the phone down on her".
The quote appeared in articles by several other news outlets yesterday, including politics.co.uk.
The Sunday Times later apologised on Twitter, blaming the mistake on a "production error":
"Due to a prod error a quote was wrongly attributed to @johnprescott. We apologise for the confusion & are happy to set the record straight."
But Prescott replied: "Typical of Murdoch newspaper to blame a production worker not the journalist. My name was used to justify big beast headline."
"So I refuse to accept this mealy mouthed apology. I want a front page retraction – due prominence – in next week's Sunday Times," he added.
Writing on his website this morning, former Downing Street director of communications under Alastair Campbell said: "The paper's claim that this was all down to a production error was as believable as many of the stories which appear in the Sunday papers.
"And the episode is a good opportunity for me to remind you of something I have said on here before – that most anonymous quotes in newspapers, particularly at the weekends, are made up."
Free daily newsletter
- Newsrewired special: emerging social platforms and why journalists should care
- A decade on from the Arab Spring: ten ways use of social media has changed in the Middle East
- How did you get your first job as a trending writer?
- Tip: Five ways to maximise audience engagement on Twitter
- Where does the buck stop for social platforms when it comes to responsible publishing?