Montague and Prescott, along with Labour MP Chris Bryant and former Scotland Yard deputy assistant commissioner Brian Paddick, had a previous bid for a review refused in February.
But this week giving his ruling in the High Court Mr Justice Foskett said the "factual complexion" of the application he was presented with was "markedly different from the picture" conveyed to the previous judge, Mr Justice Mitting.
Montague claims that he approached the News of the World with a story, but was turned down and subsequently had his phone hacked and information about the story obtained illicitly.
Foskett said that he had approved Montague's right to challenge the met, despite his individual claim looking "somewhat threadbare" at this stage.
"For the reasons I have given (at somewhat greater length than I had originally intended), I am prepared to grant permission to Mr Bryant, Mr Paddick and Lord Prescott to apply for judicial review," he concluded.
"So far as Mr Montague is concerned, for reasons I have identified in paragraph 32 above there does not, at this stage, appear to be any evidence that his name did appear in the Mulcaire/Goodman papers."
However, he added that on a "purely pragmatic basis, and with a view not to increasing costs", he had decided not to refuse permission. He did give a general warning that the merits of the case will need to be kept under review by the claimants' advisers after the evidence has been served.
"It will, I am sure, be apparent to Mr Montague and to his advisers that his individual claim looks somewhat threadbare at this stage," he added.
Acknowledging the previous, unsuccessful bid, Foskett said that the four claimants figured in "significant new information" provided by News International. He also outlined changes to the "scenario" in recent months, such as the suspension of Ian Edmondson, assistant editor, news, from the News of the World in January this year and the launch of a new police investigation.
"It was, perhaps, unfortunate," Foskett said, that the Administrative Court was not invited to delay the initial decision "in case, as might have been anticipated, there were developments of importance."
In the days following Mitting's decision to refuse the claim for a judicial review, deputy assistant commissioner Sue Akers, who was in charge of the new police investigation, called Operation Weeting, issued a statement acknowledging that some individuals had been identified "who had previously been advised that little or no information was held on them".
Speaking on Twitter Prescott said: "I look forward to receiving full and proper explanations and information as the case progresses."