The leaders of Britain's three major parties have struck a deal on press regulation, according to Harriet Harman.

She told BBC Radio 4 "an agreement" has been reached between David Cameron, Ed Miliband and Nick Clegg on a Royal Charter for a new press watchdog, backed by statute.

It is understood that Labour and the Lib Dems have accepted a watered-down version of their own demands for a press law to influence what newspapers can and cannot publish.

None of the three major parties have yet confirmed a deal has been struck. However, if Harman's report is correct, it would mark a major climbdown from the Prime Minister.

While both Clegg and Miliband had favoured the introduction of a formal press law, Cameron had opposed such a measure, arguing that legislation would impinge upon press freedom.

However the report on press ethics produced by Lord Justice Leveson said that lesiglation was essential for the new system of press regulation to work.

'No political involvement'

Harman said the new legislation will be included in the enterprise and regulatory reform bill, currently making its way through parliament. She also moved to quell fears that legislation will lead to politicians, celebrities and Whitehall cronies meddling in newspapers' operations.

The Labour deputy leader said: "It absolutely will not have politicians involved in it at all.

"That is one of the things that Lord Justice Leveson, who did an inquiry and then made these proposals, said actually - there shouldn't be tampering with the system by the press or by politicians.

"If a complaint is going to be made, it has got to be independently looked at, so the person complaining knows that actually there is a fair decision.

"And that if something is being got wrong on the front page and an apology is ordered and a correction has to be made, it is not put on page 26 but it is actually put on the front page."

Labour MP Tom Watson, who battled media tycoon Rupert Murdoch over phone hacking at the now-defunct News of the World, hailed the deal on Twitter.

He tweeted: "It looks like there is a proper deal: a Royal Charter that will be genuinely independent.Need to see the detail but it seems quite a moment."