LONDON – British politicians have finally agreed tough new U.K. press regulations that could cost offending newspapers up to £1 million ($1.5 million) in fines.

Move follows the 2011 phone-hacking scandal in which reporters working for Rupert Murdoch’s now defunct weekly tabloid The News of the World hacked a cell phone belonging to murdered schoolgirl Milly Dowler. It later emerged reporters had also listened into voice-mails of many celebrities including Hugh Grant and Sienna Miller.

Prime Minister David Cameron unveiled the proposals on Monday, after months of political wrangling in the wake of a report into the matter published last November by judge Brian Leveson.

The new regulator will be able to force newspapers to issue corrections and apologies, and impose fines of up to $1.5 million.

It will be established by a royal charter, similar to one that underpins the BBC, and can only be amended by lawmakers if there is a two-thirds majority in both the upper and lower houses of Parliament.

In other words, the idea is to uphold press freedom while also giving the regulator real teeth — without opening it up to political interference.

One of the groups lobbying for tougher regulation, Hacked Off, whose supporters include Grant and thesp Steve Coogan, welcomed the move.

The group said it believed the deal “can effectively deliver” Leveson’s recommendations for a robust, independent regulator that cannot be manipulated by newspaper owners like Murdoch.

Before the deal was struck, Grant said: “I hope that Parliament will grab this opportunity to recast the relationship between the citizens of Britain and their newspapers.

“I hope it will be brave and bring about an enduring settlement that protects the public and press freedom simultaneously.

“If MPs fail, we will all be back here in 10 years’ time with another inquiry after more newspaper abuses of innocent people.”

In July 2011, Murdoch’s plan to take complete control of U.K. paybox BSkyB fell apart when the hacking scandal emerged.