Lord Justice Leveson said that when Mr Yates was asked to review Operation Caryatid, the original phone hacking inquiry: "I regret that Assistant Commissioner Yates did not reflect on whether he should be involved in an investigation into the newspaper at which he had friends…he would have been better advised to arrange for a different officer to conduct it."
He said the "incredibly swift" dismissal in 2009 of a Guardian article suggesting there were 3,000 victims of phone hacking and a "continued defensive mindset" over re-opening the investigation contributed to concerns that the police were "reluctant" to do so because officers had "become too close to News International and its staff".
Such a perception had been "extremely damaging" to the standing of Scotland Yard.
Other officers also come in for criticism.
Andy Hayman, who was in overall charge of Operation Caryatid during his time as assistant commissioner, was "extremely unwise" to accept hospitality from the News of the World at a time when it was coming under investigation.
Mr Hayman went to dinner with Andy Coulson, then editor of the News of the World, and Neil Wallis the day before Operation Caryatid was formally launched, and this had "fuelled the perception" that a decision to arrest only one News of the World journalist and one private detective was "a specific consequence of that relationship".
The Inquiry had heard that Dick Fedorcio, the Met's former head of communications, put Mrs Brooks in touch with an officer at the Met's stables when she asked for the loan of a retired police horse in 2007.
Lord Justice Leveson said Mr Fedorcio's help "went beyond what a member of the public could expect in similar circumstances" but did not result in anything "irregular".
Sir Paul Stephenson, who resigned as commissioner after it emerged he had accepted a free stay at the Champneys health resort while he was recovering from an operation, was portrayed as a victim of circumstance.
Sir Paul came under fire when it emerged that Champneys had been represented by Neil Wallis's public relations company, Chamy Media, but Lord Justice Leveson accepted that Sir Paul was unaware of any connection between Champneys and Mr Wallis at the time.
Mr Wallis had been employed by the Met as an external PR consultant, but any suggestion that the stay at Champneys was "a reward in kind from Mr Wallis for previous favours" was "simply not borne out" by the facts.
Overall, said Lord Justice Leveson: "There is no evidence to suggest that anyone was influenced either directly or indirectly in the conduct of the [hacking] investigation by any fear or wish for favour from News International."
In a wider context, "the Inquiry has not unearthed extensive evidence of police corruption nor is there evidence…that significant numbers of police officers lack integrity".
