LONDON (Reuters) - Days before Britain's referendum on whether to leave the European Union, former Prime Minister David Cameron made an appeal to German Chancellor Angela Merkel for limits on the free movement of people, the BBC reported on Saturday.

Britons voted on June 23 to exit the EU, with the issue of immigration and control of the free movement of people from the bloc a key campaigning issue for the "Leave" camp.

As polls indicated immigration concerns were swaying the public toward supporting Brexit, the BBC said Cameron, who quit after the EU result, telephoned Merkel to ask if she was willing to issue a statement with other EU leaders agreeing to make concessions on free movement if Britain voted to stay.

The idea was eventually shelved and the BBC said Merkel had told Cameron at an EU summit after the vote that there could be no compromise on free movement within the bloc.

Andrew Cooper, an ally of Cameron who was the main pollster for Britain Stronger in Europe campaign, said the "Remain" camp had failed to respond to public fears about immigration.

"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," he told the BBC.

"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."

The issue of immigration remains one of the main sticking points ahead of Britain's negotiations with the EU about its post-Brexit relationship with the bloc.

British Foreign Secretary Boris Johnson said on Friday he had "no doubt" that a balance between overall access to the single European market and freedom of movement could be struck.

However, others in newly appointed Prime Minister Theresa May's government including Brexit minister David Davis have said Britain should not budge from an insistence on having controls on its borders.

(Reporting by Michael Holden; editing by John Stonestreet)