Police have confirmed they have received a complaint that John Prescott allegedly broke the law by having sex with his secretary during office hours.
Ms Temple (pictured with Mr Prescott in 2001) has sold her story
The complaint was sent to Scotland Yard by a retired Glaswegian police officer who said it was "not malicious".
A Metropolitan Police spokesman said it was "considering the letter".
Tracey Temple claimed she had regular encounters with the deputy PM in his office. He has admitted the affair but said many of her accounts were untrue.
A spokesman for Mr Prescott's office has said the matter of the police complaint was being looked at and that a response would be made in Parliament "in due course".
The complaint letter, sent to the Met's Commissioner Sir Ian Blair by Alistair Watson, cited the case of a Greater Manchester police officer who was given 200 hours community service after he had sex with a woman three times at her home while he was on duty.
Ms Temple, Mr Prescott's former diary secretary, claimed they had sex at his Whitehall office while they were supposed to be working.
Extracts of Mr Watson's letter, published in the Sunday Times, said: "I think in the interest of equality and justice, there is no reason why Mr Prescott and Miss Temple cannot be prosecuted.
"This is not a malicious thing. If there are rules that apply to ordinary people, somebody like John Prescott should be treated the same, or more harshly."
He also said Ms Temple should forfeit any profits made by selling her story to a newspaper to help "deter others in public employ".
Scotland Yard says a response will be given in due course.
In this week's post-elections Cabinet reshuffle John Prescott was stripped of his department, although kept on as deputy prime minister and allowed to retain his salary and grace-and-favour homes.
The decision to allow Mr Prescott to retain his ministerial perks provoked anger among some opposition and Labour MPs.