During exchanges in Prime Minister’s questions, Mr Cameron accepted comments made by Labour Scottish affairs select committee chairman Ian Davidson that the last person Scots supporting a No vote want is “a Tory toff from the home counties”.
The Prime Minister said: “I accept that my appeal does not stretch to all parts of Scotland.”
A spokesman for Mr Cameron also confirmed that the Prime Minister will definitely not take part in a TV debate with Mr Salmond.
The exchanges brought a low key and sombre PMQs to life as SNP Westminster leader Angus Robertson went on the attack over Mr Cameron’s refusal to take part in a TV debate with Mr Salmond.
A recent poll revealed that 63 per cent of Scots want a TV debate between the two men
Mr Robertson asked: “The Prime Minister’s anti-independence campaign launched an initiative this week encouraging people outside Scotland to take part in the debate. Given that – why won’t he debate First Minister Alex Salmond on television.”
But Mr Cameron hit back describing Mr Robertson as “Alex Salomond’s lackey”.
He accused the SNP of “wanting to change the terms of the debate” because they are “completely losing the arguments” on all the issues.
He said that the leader of the No campaign should debate the leader of the Yes campaign and accused Mr Salmond of avoiding debating with former Labour Chancellor Alistair Darling.
He said: “The calls for this debate show a mounting frustration among those wanting Scotland’s separation from the rest of the United Kingdom, because they know they are losing the argument. They are losing the argument about jobs and investment.
“They have completely lost the argument about the future of the pound sterling, and they are losing the argument about Europe.
“Yes of course there should be a debate, but it is a debate among the people in Scotland. The leader of the ‘in’ campaign should debate with the leader of the ‘out’ campaign.”
He added: “Of course the honourable gentleman, as the lackey of Alex Salmond, wants to change the terms of the debate, but I am not falling for that one.”
In his question Mr Davidson said it was “genuinely absurd” the leader of the No campaign against independence, Labour former chancellor Alistair Darling, could not secure a debate against Mr Salmond as the SNP leader was still hoping to face the Prime Minister in a head-to-head debate on television instead.
And reminding the House of his campaign to make sure the two aircraft carriers were built on the Clyde, he went on: “In these circumstances, does the Prime Minister agree with me that, in politics as in shipbuilding, empty vessels make the most noise?”
As the Prime Minister rose to answer Mr Davidson waved for him to sit down as cheering Tory MPs called “more, more” for the Labour MP for Glasgow South West to continue.
Turning to Mr Cameron, the MP then teased the Prime Minister about his decision to award his hairdresser Lino Carbosiero an MBE in the New Year’s honours list.
Mr Davidson responded: “There is more. Without seeking to give offence to you, can I tell you that the last person Scots who support the No campaign want to have as their representative is a Tory toff from the home counties, even one with a fine haircut?”
Mr Cameron replied: “I accept every part of the honourable Gentleman’s question. I well remember when he came to Question Time not with an empty vessel but with a model of the vessel that he wanted to be built near his constituency, and I am proud that the Government are building that vessel and, indeed, another one like it.”
On his own standing in Scottish politics he added: “I humbly accept that, while I am sure there are many people in Scotland who would like to hear me talk about this issue, my appeal does not stretch to every single part.”
But he said: “The key point that he is making is absolutely right: the reason the yes campaign head and the no campaign head cannot seem to get a debate is that those who want to break up the United Kingdom know that they are losing the argument, so they want to change the question.
“It is the oldest trick in the book, and we can all see it coming.”
After exchanges Mr Robertson said that Mr Cameron’s position on the TV debates is “incoherent”
He said: “It is his anti-independence campaign and he is now asking people outside Scotland to get involved yet he still refuses point blank to debate himself . It is time for him to put up or shut up.”
No poll ceasefire for Glasgow Games
Sport minister Shona Robison yesterday said it would be “unrealistic” for campaigners in the independence debate to call a truce during the Glasgow Commonwealth Games.
Former Labour First Minister Lord McConnell had expressed concern that referendum rows could overshadow the event.
Speaking as the minister in charge of the sporting event, Ms Robison insisted politicians from all parties were “mature enough to recognise” the Games were “hugely important” for Scotland and said no-one would risk jeopardising their success.