The Prime Minister - who made an impassioned plea to Scots to reject independence saying it would ‘break the UK family apart’ - is alleged to have made the comments to former Deputy Prime Minister Nick Clegg just days after the historic vote.
Ex-Lib Dem Schools minister David Laws, writing in Coalition, his recent book about the coalition government, said: “Over the weekend, Nick Clegg spoke to David Cameron. It was a tense conversation.
“Nick Clegg warned that the referendum aftermath was in danger of becoming a complete disaster.
“He said bluntly that the Prime Minister was in danger of guaranteeing the break-up of the UK, with the only beneficiaries being the SNP.
“‘Look Nick’, said David Cameron impatiently, ‘I just don’t care. We’ve only got one Conservative MP north of the Border. Let Labour sort it out. It’s now their problem.’
“Nick Clegg and Danny Alexander were both furious. ‘I used to disagree with the Conservatives but at least respect them,’ Nick Clegg told me a week later. ‘But now I have contempt for what they have done. It is all so bloody short-termist and short-sighted.’”
However, Downing Street has dismissed the claims as ‘tittle-tattle’, with a spokesperson telling The Times newspaper: “The evidence is there in what we have done: produced a Scotland Act, delivered the Vow and created a powerhouse Scottish parliament.”
But an SNP spokesperson insisted the revelation would harm Scottish Conservative leader Ruth Davidson’s campaign for the Holyrood elections.
Ms Davidson’s party and Scottish Labour were reportedly neck-and-neck in the race for second place according to a recent poll.
The SNP spokesperson said: “Ruth Davidson’s election claims are badly undermined by the revelation that her boss simply ‘doesn’t care about Scotland’”.
Leader of the Scottish Liberal Democrats Willie Rennie added: “The Tories aren’t Unionists, they are divisionists.
“Whether it’s portraying Scotland as a pickpocket or taking £7 billion out of its budget, the Tories just care about themselves and their party.”