Former Supreme Court president Lord Phillips of Worth Matravers has been asked to advise on the establishment of a new press regulator, amid much scrutiny over the impact of Lord Justice Leveson's recommendations for media reform.

Phillips has been asked by Press Complaints Commission (PCC) chairman Lord Hunt to work alongside former Labour culture secretary Lord Smith and Simon Jenkins, the former editor of The Times, to help devise the new regulatory body.

Following his inquiry into the culture, practice and ethics of the media, Leveson's long-awaited report last month recommended that an independent self-regulatory body governed by an independent board be put in place, effectively revamping the existing PCC, which is currently responsible for press regulation.

The appointment for Phillips comes after he retired from the Supreme Court at the end of September this year. He has returned to his former set Brick Court Chambers as an arbitrator.

Meanwhile, Matrix Chambers' Antony White QC and Alexandra Marzec from 5RB have been instructed by a host of national newspapers to advise on the proposed new arbitration system put forward by Leveson in his report.

White and Marzec are advising in-house counsel at newspapers including: The Guardian, The Independent, The Times and the Financial Times on the proposed new system and how it might work in practice.

Leveson has recommended that an arbitration system for civil legal claims against the press should be introduced to allow complaints to be dealt with "quickly and inexpensively" and allow "frivolous or vexatious" claims to be struck out early.

He also suggests that the arbitration system should be used as an incentive for publishers to become members of the industry's new independent regulatory body, with those opting not to participate unable to use the arbitration system or recover any costs from the courts, even if successful.

In-house counsel from the same publications have also been consulting on other proposals included in Leveson's report before endorsing them.

Editors of the newspapers met at the Delaunay restaurant in central London to discuss all of the proposals earlier this month, with concerns raised over Leveson's recommendations for third-party complaints and the suggestion that the new regulator could intervene in a case of allegedly discriminatory reporting in "the spirit of equalities legislation".

The Guardian's director of editorial legal services, Gill Phillips, told Legal Week: "The editors have asked the in-house lawyers to advise them on setting up the arbitration aspects of Leveson's recommendations. We are discussing this amongst ourselves with the assistance of external counsel.

"Any scheme needs to be quick, cheap, accessible and efficient and those things don't always come out on the same line, so we're trying as quickly as we can to come up with a proposal that will ensure all of these things to then put to our respective editors for them to take forwards."