"I have asked the Metropolitan Police to give the committee a full explanation of why they took the decision to invoke the Official Secrets Act and to provide us with a timeline as to exactly who was consulted," said Vaz.
Vaz said he also wanted to know what action the force had taken to prevent further leaks.
The left-leaning Guardian revealed in July that the voicemail of Milly Dowler, a teenage murder victim, had been hacked by the News of the World, a Sunday tabloid owned by the Australian-born Murdoch's News International.
The story led to a public outcry and Murdoch closed the News of the World shortly afterwards, while Scotland Yard's chief and another senior officer resigned over their links to Murdoch's empire.
In August, a policeman working on the probe was arrested over the unauthorised disclosure of information.
On Friday the Metropolitan Police said it had applied for a production order against The Guardian and its reporter Amelia Hill over claims that a senior detective leaked the information about Dowler to the paper.
The Met backed down late Tuesday after an outcry in the British media and criticism from several quarters including film star Hugh Grant, himself a hacking victim, who described the police actions as "worrying and deeply mysterious".
Simmons admitted on Wednesday that the force was wrong to have said in its court application last week that it wanted to seek evidence of offences connected to breaches of the Official Secrets Act, among other laws.
"The view I came to when I looked at the matter was that the Official Secrets Act was not an appropriate element of the application, and that was the basis of the decision to withdraw the application at this time," Simmons told the BBC.
The police officer denied that the case had harmed Scotland Yard, but said the changing relationship between the police and the media in Britain was taking police into "uncomfortable territory".
Guardian editor Alan Rusbridger welcomed the decision to drop the application, but criticised police for saying that they would still pursue the investigation into the alleged leaks by police staff.
"They should just stop that," Rusbridger told the BBC.
"These are reporters who are just doing their ordinary business. If you are going to criminalise reporters who talk to public officials on an unauthorised basis, you would be locking up most journalists in Britain."
News International is SET to pay £2 million ($3.1 million, 2.3 million euros) in compensation to Milly Dowler's family while Murdoch himself will make a donation of £1 million to charity, reports said Monday.
The scandal has prompted a series of parliamentary committee hearings, including one in July during which Murdoch was hit in the face with a custard pie. A judge-led public inquiry into the issue is also underway.