The officers, accused of leaking details about pornographic material found almost a decade ago on Mr Green’s computer, were warned they could even face prosecution.
A clearly angry Prime Minister said she expects alleged breaches of professional conduct “to be taken seriously” and other Tory MPs said the former officers deserved criminal action.
Metropolitan Police Commissioner Cressida Dick said Scotland Yard had referred the two retired officers to the Information Commissioner’s Office over possible breaches of data protection legislation.
Mr Green, made First Secretary by Mrs May after the election, was dramatically sacked from the Cabinet on Wednesday after admitting he made “misleading” statements claiming he knew nothing about the discovery of pornography on his computer during a 2008 investigation into Home Office leaks.
Allies of the Prime Minister said she had no choice but to act after a Cabinet Office inquiry found he had breached the ministerial code.
But Conservative backbenchers said his misconduct was “dwarfed” by the actions of former Met assistant commissioner Bob Quick and ex-detective constable Neil Lewis in passing to the media confidential information obtained during a police inquiry.
Speaking during a visit to Poland, Mrs May made it clear she shared anger about the way details of the 2008 police inquiry had entered the public domain. Mr Green was a shadow minister for the Tories, who were in opposition at the time, when Labour ministers ordered an investigation into a series of damaging leaks which led to his computer being confiscated by police.
The pornography, which was legal, was discovered as a result of the controversial action.
Nine years later its existence was used against Mr Green by the retired police officers in what Tory MPs are calling “a vendetta”.
Mrs May said: “I share the concerns that have been raised across the political spectrum and I expect that issue to be properly investigated, to be taken seriously and to be properly looked at.”
Conservative MP Chris Philp told the BBC: “I think they should be investigated for misconduct in public office. That is a criminal offence.
“What they have done is completely wrong.
“It undermines trust in the police. How can any of us trust giving information to the police if senior officers leak in this way?”
Appearing before the London Assembly, Yard Commissioner Cressida Dick said the ICO was the right body to take the inquiry forward.
“We are disappointed to see that it appears that former colleagues have put into the public domain via the media material that they appear to have had access to as part of the confidential investigation,” she said.
“I have a very strong view that the responsibility that goes with being a police officer or a member of police staff is very clear in relation to people’s personal information.”
Information Commissioner Elizabeth Denham said ICO’s investigation would look at whether the individuals concerned had “acted unlawfully by retaining or disclosing personal data”.
She said: “These are serious allegations and we are investigating to determine whether the law has been broken and what further action is necessary.”
Mr Green strongly denies looking at pornography on his work computer and has also rejected another allegation – that he sexually harassed journalist and former Tory activist Kate Maltby.
But he accepted he had breached the code of conduct. Health Secretary Jeremy Hunt said that Mrs May had no choice but to sack her lifelong friend but acted with a “very heavy heart”.
Trade minister Mark Garnier – investigated after it was revealed he called a former secretary “sugar ****” and also asked her to buy sex toys – was found not to have breached the ministerial code yesterday and remains in his post.