The decision to drop all charges due to lack of evidence followed headlines that dubbed her as 'Saline serial killer' and the 'Angel of Death', which could be seen as pushing the boundaries of the Contempt of Court Act.
Clifford said: 'If the Press Complaints Commission was doing its job properly then people like Rebecca wouldn't be coming to me - they would be going to the body set up to protect them.'
The call for stronger press scrutiny mirrors those in response to the News of the World hacking scandal.
This year, the Daily Mirror was fined £50,000 and The Sun £18,000 for contempt of court for stories about Christopher Jefferies, the Bristol landlord of murdered Joanna Yeates.
The case suggested that Attorney General Dominic Grieve was taking a tougher line over contempt.
Melissa Davis, director of legal PR specialists MD Communications, said she hoped Grieve's actions would 'prove a timely reminder to media and the authorities that delivering a fair trial is the best way to serve the public interest and the rights of accused'.
But others felt the coverage of Leighton's case suggested that the threat of contempt remained a limited deterrent.
Burson-Marsteller MD Clarence Mitchell, who worked with Gerry and Kate McCann when their daughter Madeleine went missing, said: 'The laws covering contempt of court and defamation have been in place for generations. However, the capacity for "trial by media" has never been greater.'
Clifford added: 'The risk of missing a scoop far outweighs contempt of court charges for today's media. The press is so entrenched in circulation battles that all reasoning and media law know-how goes out the window.'
Despite the inevitable legal restrictions in criminal cases, PR advisers (see below) suggested a proactive approach.
Clifford said he wanted to see Leighton on TV, radio and in the press talking about 'how she and her family have been badly treated by the media'.
5 July Contempt proceedings against The Sun and Daily Mirror over their coverage of the murder of Joanna Yeates.
20 July Stepping Hill acting ward sister Rebecca Leighton is arrested. Next day's headlines: Daily Mirror: 'Saline serial killer'; Daily Star: 'Nurse in angel of death quiz'.
22 July Leighton charged over deaths.
29 July Daily Mirror fined £50,000 and The Sun £18,000 for contempt of court. Eight papers pay Christopher Jefferies libel damages and publish apologies.
2 September Charges against Leighton dropped due to lack of evidence.
6 Weeks Rebecca Leighton spent in Styal Prison until charges were dropped*
£1m Amount she could win by suing police for wrongful arrest*
£50k Contempt fine for Daily Mirror over reports about Christopher Jefferies**
8 Number of newspapers that agreed to pay Jefferies libel damages***
Source: *various; **The Guardian; ***tabloid-watch.blogspot.com
HOW I SEE IT
Top PR professionals advise on the best way to navigate a hostile media
ALAN EDWARDS, FOUNDER, OUTSIDE ORGANISATION
Last year our client Naomi Campbell was involved in the 'Blood Diamond' trial of Charles Taylor and we were faced with some very difficult media perceptions. The most immediate problem we faced was making it clear to everybody that Naomi wasn't on trial at all and was merely a witness to events.
We also worked for Asher D from rap group So Solid Crew on firearms charges in Southwark Crown Court.
In these situations, it's important to counter issues point by point and correct each inaccuracy as quickly as it arrives. Be methodical: anticipate the worst questions and accusations that could be made against your client and try to counter claims as quickly and as openly as possible. It may cause some short-term media pain, but it is less of a nightmare than trying to get the genie back in the bottle.
CLARENCE MITCHELL, MANAGING DIRECTOR, BURSON-MARSTELLER
When taking on a client who has undergone an ordeal like Rebecca's, a PRO needs to establish quickly the facts, counsel complete transparency and then develop and rapidly deploy a fact-based rebuttal and corrective narrative, through both on and off-the-record guidance.
Nor should the PRO and client be afraid to engage the elements of the media that have been most hostile. They should be targeted first. Reputation lives or dies on those battlefields and that is where public perception of the client must start to be rebuilt.
A willingness to engage, a compelling, fact-based balancing narrative, underpinned by utter honesty, will generally start to move public opinion positively - and get your client out there while the public and media are still listening.