This royal charter will only be changed with a two thirds majority of MPs and peers.
However Mr Cameron opposes the move and wants to establish a regulator by royal charter.
They said the decision did not mean the government was giving up on a cross-party royal charter.
Mr Cameron is opposed to enshrining the royal charter in law, saying it will harm press freedom.
Labour is expected to table amendments designed to produce what the party describe as "a Leveson-compliant royal charter".
Government sources told the BBC they prefer for the royal charter to be agreed without recourse to legislation.
The newspapers opposed the idea of a regulator backed by a royal charter, and have revealed an alternative plan.
BBC: Leveson report: Newspapers reject press regulation plans
The new director general's first priority will be to prepare the BBC for the review of its Royal Charter.
The prime minister has indicated that he would want to take the royal charter to the Privy Council in May.
Holyrood's party leaders will meet later today to decide whether or not to endorse the proposal of a royal charter.
White Swans are protected by a royal charter, but if the Swans go down it may just signal their extinction.
But much remains to be studied before the royal charter can be accepted as the foundation stone of new regulation.
The ferries are protected by a Royal Charter and it would need an act of parliament to end the service.
He added that the idea of a royal charter was "not ideal" and "pretty meaningless" the way it was currently drafted.
The royal charter created in the wake of Leveson will create a so-called recognition body to oversee a new press regulator.
The Goldsmiths Company, which earned its royal charter in 1327, has seen a few changes in the techniques used by jewellers.
In 1660, the Royal Society of London for Improving Natural Knowledge was founded by Royal Charter of King Charles the Second.
He added the Royal Charter would be in place to ensure the system was independent and not to exercise control itself.
Among the items in the archive is the Royal Charter of Carlisle from 1316, which bears the seal of Edward II.
The royal charter says it covers websites that provide news-related material, but there is some confusion as to what that really means.
Cross-party proposals for a royal charter to underpin press regulation following the Leveson report are to be delayed, Downing Street has said.
Committee convener Stewart Maxwell said they had concluded that a UK-wide Royal Charter could give the press "one final opportunity to change".
Months ago the government proposed that a Royal Charter rather than a legally based system was the key to unlocking a deal.
The industry's proposal is closely based on the draft royal charter published on 12 February following negotiations with national and local newspapers and magazines.
BBC: Leveson report: Newspapers reject press regulation plans
Trading in Surrey Street, which is at the heart of the Old Town, began after the area was granted a Royal Charter in 1276.
Wootton Bassett Town Council has confirmed that any surplus money raised through donations to the royal charter celebrations will be donated to various forces charities.
It is understood they have still to agree whether a royal charter needs to be underpinned by legislation - one of the report's main recommendations.
The Conservatives opposed regulation backed up by statute, arguing a Royal Charter was the right way to provide legal backing for any new press regulator.
He added that this could delay the abolition of some of the quangos, as could the fact that some of them were protected by royal charter.
Mr Llewellin said he preferred reform of the voluntary Press Complaints Commission code and described the idea of a royal charter as "perverse" in the Scottish context.
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