Shadow culture secretary Harriet Harman argued today that the Lord Chief Justice was the best person to oversee "independent" regulation of newspapers.
She launched Labour's draft parliamentary Bill on press regulation, which was first leaked to the liberal Establishment paper the Guardian on Sunday night.
The Bill proposes a "recognition panel" of advisers headed by the Lord Chief Justice to keep watch over a press self-regulatory body and to determine whether the body is functioning properly every three years.
Haggling continued at Westminster over implementation of the tame Leveson report into press ethics, which waved a feather duster at the scandal sheets and let politicians and police off the hook.
Labour's draft Bill said members of the regulatory body should be people who are "demonstrably independent of executive and Parliament," with a majority "demonstrably independent of the press."
No serving editor would be allowed to sit on the board.
Newspapers should be encouraged to join the new system through the offer of lower levels of high court damages and costs, said Labour.
The proposed Bill stipulated that ministers and public functionaries must uphold freedom of the press and avoid "improper political influence over the media."
Labour has dropped its original proposal that broadcasting regulator Ofcom should act as the body overseeing the press regulator. Opposition leader Ed Miliband discussed Labour's proposals with Lib Dem leader Nick Clegg and with some Tory MPs who support Labour's policy of statutory backing for "independent press regulation."
Further cross-party talks this Thursday will involve Culture Secretary Maria Miller, who is working on a government draft Bill following PM David Cameron's professed opposition to "writing press regulation into the law of the land."