Tom Watson's Leon Brittan letter received after police interview
A letter by MP Tom Watson demanding Lord Brittan be interviewed about a rape allegation was only passed to police after the former home secretary was questioned, prosecutors say.
Labour's deputy leader has been accused of inappropriately intervening in the case.
Lord Brittan died in January without being told he had been cleared of the allegation.
Mr Watson will be questioned over his actions by MPs next week.
The Crown Prosecution Service (CPS) found in July 2013 that there was not enough evidence for a prosecution over the claim Lord Brittan had raped a 19-year-old female student in 1967.
In a letter to Director of Public Prosecutions Alison Saunders in April 2014, Mr Watson complained that the "investigation into the serious allegations in this case was dropped before the suspect was interviewed".
He also said he was "driven to the unpalatable conclusion that the identity of the alleged perpetrator - Leon Brittan - may in some way have influenced treatment of the case".
The letter was received by the CPS in late April and details of it were widely reported in the media in the middle of May.
The letter was passed to the police on 2 June, two days after they had interviewed Lord Brittan.
The CPS has released a statement saying it did not ask the police to reopen the investigation as a result of Mr Watson's letter.
It said it had forwarded Mr Watson's letter to the Metropolitan Police, saying this was normal practice, and that Lord Brittan had already been interviewed by the Met by the time it received the letter.
"It is for the police to decide whether or not, or how, they will investigate an allegation that is referred to them," the statement added.
"The CPS has no power to direct them and did not seek to do so."
The Home Affairs committee, chaired by Labour MP Keith Vaz, has asked Mr Watson to "provide clarification on a number of issues" on 21 October.
The committee, has also asked representatives of the Metropolitan Police to appear.
On Monday, Mr Watson was urged to apologise for his pursuit of the Lord Brittan allegations, by Tory MP Sir Nicholas Soames, who said he had "vilely traduced" the former home secretary.
In response, the Labour MP told the Commons he had been right to raise the issue.