It is not only David Cameron and Rupert Murdoch who are caught in the sticky web of the phone-hacking scandal. Scotland Yard too remains tangled in troubling questions revived by evidence disclosed in the Old Bailey trial that ended last week.

The questions remain unanswered because while the Yard's leadership has run a sprawling inquiry into allegations of crime by journalists and public officials, it has opted not to commission any kind of investigation into what went wrong under its own roof.

All the questions revolve around Scotland Yard's five years of failure to deal with allegations of crime in Murdoch's newsrooms before a new inquiry, Operation Weeting, finally took on the job. The scale of the Yard's failure to investigate or to disclose what was known was writ large in the evidence Weeting supplied to the Old Bailey trial.

While the original inquiry named only eight victims of Glenn Mulcaire's phone hacking, Weeting found Mulcaire's own handwritten notes suggested he had targeted 6,349 people either to intercept their voicemail or to "blag" their confidential data. The original inquiry led to just two arrests. Weeting and its offshoots have arrested or interviewed under caution some 210 people.

The central question is whether that failure was in any way connected to the Yard's links with Murdoch's UK company, then known as News International; or to any personal links between Yard officers and Murdoch employees. Fragments of new evidence from the trial and from Guardian inquiries raise more questions. They fall into two timeframes.

Private investigator Glenn Mulcaire was jailed for phone hacking. Photograph: Fiona Hanson/PA

The first covers the period from January 2006 to January 2007 when the Yard ran Operation Caryatid, the original inquiry into a complaint from Buckingham Palace that somebody was listening to the voicemail messages of the royal household. On 8 August 2006, Caryatid arrested the News of the World's royal editor, Clive Goodman, and the paper's specialist phone-hacker, Glenn Mulcaire.

At the Old Bailey trial, Goodman told the jury that within 48 hours of his arrest, he saw the start of a campaign to persuade him to say he was a "lone wolf" who had hacked the royal phones without the knowledge of anybody else at the paper and that nobody else from the paper was involved in any other hacking. This "lone wolf" theory was a lie, as the trial exposed in painful detail. It would also have been apointless lie in the event of any risk that Scotland Yard would arrest other journalists. No other journalists were arrested by Caryatid.

During the trial, Goodman claimed that, following his arrest, Andy Coulson on several occasions suggested that he was directly or indirectly in contact with a source who knew what the police were doing and who was suggesting that they did not want to "go any deeper than me and nobody wanted it to end up in a jail sentence." Coulson denied saying this. Even if he did, it is possible that he was misleading Goodman in an attempt to persuade him to plead guilty. The question is whether there really was a source who enabled Coulson to know what the police were planning.

Six weeks later, on 15 September, a News International lawyer emailed Coulson with a summary of information he said had been provided to Rebekah Brooks by "the cops". The email – disclosed in unredacted form at the trial – included an apparently accurate account of some of the evidence collected by Caryatid and the suggestion "they are not widening the case to include other NoW people but would do so if they got direct evidence". The email said that so far the only evidence found against journalists other than Goodman was circumstantial.

The trial heard that this message was written as a result of a meeting at the RAC Club in London between Brooks and a Caryatid officer, DCI Keith Surtees, who had been tasked to tell her that her phone had been hacked by Mulcaire and to invite her to make a statement for the prosecution. Brooks declined to do so. The question here is whether Surtees was instructed not simply to ask for her cooperation but also to give her a briefing about Caryatid's progress and intentions. The Independent Police Complaints Commission investigated and found that Surtees had done nothing wrong. Scotland Yard declined to answer Guardian questions about it.

At around this time, according to evidence at the Leveson inquiry, the Yard decided to close down Caryatid. The precise timing and justification for this decision are not known: it was not recorded in writing.

The effect of this was that there was no further inquiry into evidence gathered by Caryatid that appeared to implicate other NoW journalists; a breach of the Yard's undertaking to the Crown Prosecution Service that officers would ensure "all potential victims" were informed; and a failure to follow evidence which suggested the NoW may have been involved in making corrupt payments to police officers including some involved in the security of the royal family and of the Witness Protection Programme.

Clive Goodman, the former royal editor of the News of the World, arrives at the Old Bailey in March 2014. Photograph: Andrew Winning/Reuters

In November 2006, Goodman and Mulcaire pleaded guilty without implicating anybody else at the newspaper.

After examining this history in detail, Lord Justice Leveson concluded that the Caryatid team had made mistakes in handling victims of the hacking and had failed to follow leads to other perpetrators but had acted in good faith, primarily because officers had to deal with far more serious crime involving terrorist plots to commit mass murder. That conclusion is clearly well-founded. Specifically, there is no evidence that any Caryatid officer showed any fear or favour towards News International.

However, the objective fact is that Scotland Yard's conduct enabled News International's coverup to succeed. Here, there are two key questions. Why was the hacking inquiry not passed to another squad to be completed? And was that decision in any way influenced by a desire to placate Murdoch's company?

Scotland Yard has opted not to try to answer any of these questions.

The Guardian front page of 9 July 2009. Photograph: Guardian

The second timeframe runs from 9 July 2009, when the Guardian published its first story about the true scale of the hacking, to July 2011, when it disclosed that Milly Dowler's phone had been hacked. During that time, Scotland Yard presented press, public and parliament with a version of events that has proved to be false.

This included repeated denials that the Yard held any evidence that Mulcaire had targeted the then deputy prime minister, John Prescott; repeated claims that detectives had approached all potential victims of Mulcaire's hacking; and claims they had pursued all available leads. All of these statements proved to be false.

The Yard also failed to disclose that Caryatid had been closed down without completing the original investigation; and that News International had obstructed officers' work.

The Old Bailey trial disclosed a new fragment of evidence that remains unexplained and unexplored. This involved the celebrity PR Max Clifford, who was one of the eight hacking victims and was named at the sentencing of Goodman and Mulcaire in January 2007. Soon after the Guardian's first story, in July 2009, Clifford sued the NoW on the basis that somebody at the paper must have conspired with Mulcaire to intercept his voicemail.

On 14 September 2009, a deputy master in the high court ordered Scotland Yard to disclose relevant evidence, including the notes Mulcaire had made as he targeted Clifford. The Yard said it would do so by 23 November.

The then acting deputy Metropolitan police commissioner, John Yates. Photograph: Stefan Wermuth/Reuters

On 5 November, the assistant commissioner who had inherited responsibility for the hacking case, John Yates, dined at the Ivy with the then editor of the News of the World, Colin Myler. It's unclear exactly what was discussed at that dinner, but the Yard missed the deadline for disclosing Mulcaire's notes and, when they finally did so, on 7 December, the name of the NoW journalist who had tasked Mulcaire to hack Clifford had been blacked out, as had much of the rest of the notes.

The fragment of evidence disclosed at the Old Bailey trial concerned a meeting held at the NoW's east London office on 20 January 2010 to discuss the Clifford case. The jury were shown a record of the meeting. This noted that when the police disclosed their evidence on Clifford, "there was nothing there". The record then continued with a remark attributed to Myler: "CM said that Andy Hayman and John Yates had indicated to him previously that this was probably going to be the case."

Contacted by the Guardian recently, Myler declined to comment.

The first question here is whether that record is accurate. It may not be. Andy Hayman was the assistant commissioner during the first timeframe. He was responsible for Operation Caryatid although he had no day-to-day role in its conduct. But he had left Scotland Yard in December 2007. An investigation might establish whether Hayman had any means of discovering how the Yard was planning to respond to the order to disclose Mulcaire's notes about Clifford. Beyond the question of its accuracy, the record of that meeting raises questions. Why did Scotland Yard choose to redact Mulcaire's notes so heavily? The high court ordered a less redacted version, although the case was then aborted when Clifford accepted an offer from News International of guaranteed income of £600,000 plus his legal costs.

Did Hayman, Yates or anybody else at the Yard provided information about their handling of the case to Myler? Hayman and Yates declined to comment but Yates's friends say he would not have had access to the detail of the case and would not have disclosed anything improper.

Andy Hayman appears before Commons home affairs committee in 2011. Photograph: Pa

As the Leveson inquiry heard, both Hayman and Yates were in the habit of sharing drinks and meals with journalists, including some from the News of the World. Coulson himself previously has said he was on "not unfriendly terms" with Hayman. Yates counted another senior journalist from the paper as a personal friend. The evidence of the social contact was disclosed at the Leveson inquiry. Leveson found that it had had no impact on decisions which they made and that, although the two men had made mistakes, they had acted with integrity. Both Hayman and Yates have also been criticised for public comments which they made about the extent of the hacking at the News of the World. This began as a reaction to the Guardian's first story, on Thursday 9 July, when Yates held a press conference outside Scotland Yard. He said he had been asked "to establish the facts" and went on to read a statement that challenged the core of the Guardian account and has since proved misleading. He said no further investigation was required. Two years later, when the scandal reached its climax, Yates apologised for his approach, saying he should have done more and that his decision not to reopen the investigation was "pretty crap".

In the background, after resigning from Scotland Yard, Hayman had gone to work for News International as a columnist for the Times, which bought the serial rights to his memoirs. Two days after Yates's statement, on 11 July, he published a Times column in which he said that Caryatid "had left no stone unturned". He did not say that the investigation had been closed down without completing the job.

He went on to say that Caryatid would have pursued "the slightest hint that others were involved". The Old Bailey trial disclosed that Caryatid had done the opposite, for example opting not to pursue evidence of the possible involvement of journalists Greg Miskiw and Neville Thurlbeck, who have since pleaded guilty to conspiring to intercept voicemail. Hayman told the Leveson inquiry that he had written his column from memory without having access to any of the original paperwork.

The following week, on 15 July, Hayman went to a leaving party for a senior NoW journalist from the News of the World, at the Century Club on Shaftesbury Avenue in London. One guest has told the Guardian Hayman approached Tim Toulmin, then director of the Press Complaints Commission, who was standing by the bar, and said words to the effect that: "I can't believe this Guardian thing. Such a lot of fuss about it. I have seen the file. There is nothing in there, just a handful of names."

In November, a PCC report accepted Goodman and Mulcaire were the only culprits and added that "the Guardian's stories did not quite live up to the dramatic billing they were initially given".

Over the two-year timeframe, Yates repeated his misleading version of events to two Commons select committees and visited the Guardian to complain to the editor, Alan Rusbridger, about the paper's coverage. Later, he threatened to sue the Guardian for publishing claims that he had misled parliament. Yates and Hayman specifically denied that Prescott had been a victim even though Caryatid in August 2006 had found evidence Mulcaire had been intercepting his voicemail from the phone of his special adviser, Joan Hammell.

The home affairs select committee criticised Hayman for his "cavalier attitude" towards his social contact with News International staff being investigated by his detectives and suggested this had "risked seriously undermining confidence in the impartiality of the police". They also accused him of "deliberate prevarication in order to mislead the committee".

Leveson found that Yates had adopted an "inappropriately dismissive and close-minded attitude" to the scandal and had been dogmatic and defensive in his comments.

Neither the select committee nor Leveson concluded Hayman, Yates or anybody else at Scotland Yard had let their judgment be influenced by contact with or fear of News International. Leveson concluded that although there had been "a series of poor decisions, poorly executed", there was no evidence to challenge the integrity of the senior police officers concerned.

On the specific questions raised by the new information from the Old Bailey trial, there is no evidence at all – no phone records, no diaries, no internal memos, no expenses records, no interviews with the key players – because Scotland Yard has failed to commission the inquiry which might have found it. The questions hang there, looking for an answer.