The then prime minister called Mrs Merkel in the days before the referendum vote last month as opinion polls showed voters moving towards Leave after the Government again missed its target for cutting net migration, according BBC2’s Newsnight.
However the plan for European leaders to issue a statement promising concessions on the free movement issue was said to have been abandoned amid fears it could be portrayed as a sign of weakness by the Vote Leave campaign.
The pollster Lord Cooper of Windrush, a close ally of Mr Cameron, told the programme: “The people who are very, very concerned about immigration, what they wanted was purely and simply for the UK to be able to have total control of its borders and total control of the flow of people into this country. And we didn’t have an argument that could remotely compete with that.
“It meant we couldn’t really engage in the campaign on that vital issue. We didn’t have much option but to keep trying to pivot back to the economic risks.”
Lord Cooper also described how a claim by the then chancellor George Osborne that leaving the EU would cost the average household £4,300-a-year was quietly dropped.
“The problem with that figure - the £4,300 - was firstly it sounded implausibly large to the ears of most people. Secondly it sounded strangely specific,” he said.
“The figure was sort of humanely phased out because we found when we tested the reaction in focus groups, we found people just rejected it. They didn’t believe it.”