Downing Street has admitted that Nick Clegg has a veto over David Cameron's plan to establish a royal charter on press regulation because he is president of the body that would have to approve the measure.

The prime minister is due to publish his plan for the royal charter, though No 10 admitted it cannot come into force without the agreement of the deputy prime minister who is lord president of the council. He is the cabinet minister who leads on the privy council that would establish the royal charter.

Cameron's proposal is due to be published on Friday afternoon, and comes after all-party talks on implementing the Leveson report into press regulation collapsed on Thursday. The prime minister is to table amendments to the crime and courts bill in the commons on Monday that would allow exemplary costs and damages to be imposed on media organisations that do not sign up to a press regulation body established by the royal charter.

Ed Miliband, the Labour leader, and Clegg, who support exemplary damages, will table their own amendments to guarantee the independence of the new body. They would also like the royal charter to be underpinned in statute.

The prime minister's spokesman dismissed this. "The prime minister's view is that the royal charter does not require [statutory underpinning]," he said.

Downing Street said the prime minister will publish his own, rather than government, proposals for the royal charter because he does not yet have the agreement of Clegg. The No 10 spokesman admitted this means that no royal charter could come into force without the agreement of Clegg.

"Yes, a royal charter would need that agreement [of the lord president of the council]," the spokesman said. "What the prime minster wants to do is go and secure support for his approach which means the two amendments – on exemplary costs and damages – and then making the case for the royal charter."

Downing Street indicated that the prime minister would expect Clegg to sign up to the royal charter on his terms if the Labour and Liberal Democrat amendments are rejected by MPs."

Royal charters progress on an agreed basis," the spokesman said. "The prime minister ... has a workable solution. He is putting that forward ... If that is successful he will press for the adoption of the royal charter. Those who might disagree would have to explain why they didn't want a workable system of press regulation."

But No 10 said Cameron would respect the will of parliament if the Labour and Lib Dem amendments were passed. "Parliament is sovereign," the spokesman said.

This raises the possibility that Cameron will have to accept a royal charter on Labour and Lib Dem terms if he loses the vote. There are 304 Tory MPs and a total of 314 Labour and Lib Dem MPs.