Arday had resigned earlier in August as a professor of sociology of education following the accusations, which had rocked the world of academia.
He was found unresponsive by the ambulance service at a property in Battersea, south London, on Friday.
"Sadly, a 41-year-old man was pronounced dead at the scene. His next-of-kin have been informed and are being supported by officers," the Metropolitan Police said in a statement sent to Reuters.
The statement did not name the man, in line with the force's usual practice.
The Telegraph, Times and Sky News linked the statement to Arday.
"At this time his death is being treated as unexpected but is not believed to be suspicious. The case is being investigated by officers from the Met's Central South Command Unit. A file will be prepared for the coroner," the police said.
Arday, who became Cambridge's youngest black professor in 2023, quit following a series of media reports alleging he plagiarised his PhD thesis -completed at Liverpool John Moores University - and other research.
Further questions were asked in the press about the truth of other claims he made, including saying he ran 600 miles in six days, completed 30 marathons in 35 days and that he had raised £5.5 million for charity.
An investigation at Liverpool John Moores University cleared Arday of wrongdoing.
On July 24, the Times of London published an analysis of Arday's 2015 PhD thesis highlighting what it said were multiple examples of passages that were "identical or near-identical" to an earlier paper written by another researcher.
Cambridge initially stood by Arday, saying the plagiarism allegations had been investigated by Liverpool John Moores University, which awarded Arday's doctorate.
The university then changed its stance and said it opened an investigation "following new information about Professor Arday's qualifications and honorary appointments".
Durham and Glasgow universities are investigating the circumstances around Arday's appointment to academic posts there and Cambridge's Jesus College has accepted his resignation from his fellowship.
Arday said in his open resignation letter that the "only way to bring this chapter to an end is to step away".
"This decision should not be interpreted as a loss of faith in scholarship or in the values that first brought me to Cambridge," he said.
"Nor should it be mistaken for an acceptance of the narratives that have surrounded me.
"It is simply the decision of someone who has reached the limits of what any person should reasonably be expected to endure."
Over the weekend, he cancelled events promoting his forthcoming memoir.
Publisher Simon & Schuster previously said the book, Great And Unfortunate Things, would be published in the UK on August 27.
This week the University of Cambridge said it would run an independent review of "all relevant processes" alongside an investigation into how Arday was appointed by its Faculty of Education.
Last week, the university confirmed it would continue its investigation into the circumstances around Arday's "appointment and tenure" after he quit, adding that findings will feed into a review of the process for appointing senior roles.
Dozens of academics at the prestigious institution signed a letter calling for an independent inquiry into the processes around his appointment.
with PA and AP
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