LONDON (Reuters) - British voters have moved towards voting to leave the European Union in next month’s referendum according to two surveys by polling firm ICM, surprising investors and sending sterling sharply lower.

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The “Out” campaign stood three points ahead of “In” in each of the two surveys for the Guardian newspaper, one of which was conducted online and the other by telephone.

They were conducted over three days to Sunday after official figures showed on Thursday that British net migration hit the second highest level on record last year. Last week, leaders of the Out camp turned their focus back on migration.

Britons will vote on June 23 on whether to remain in the 28-member EU, a choice with far-reaching consequences for politics, the economy, defence and diplomacy in Britain and far beyond.

From U.S. President Barack Obama to the International Monetary Fund, a host of world leaders and international organisations have cautioned British voters about the risks of leaving the bloc it joined in 1973. The Bank of England has said a British exit, or Brexit, could tip the economy into recession.

Despite the warnings, Out has appeared to gain traction by focusing on the issue of migration. Many voters are concerned about the strains placed on schools, hospitals and housing from people moving to live in Britain.

ICM said the polls published on Tuesday gave Out its first lead in one of its telephone surveys.

Telephone polls have previously tended to give the In campaign a comfortable lead and the sharp swing wrong-footed financial markets, sending sterling to a one-week low against the U.S. dollar.

Polls conducted over the Internet have largely suggested a tighter race but ICM’s latest weekly online poll - separate to its phone survey - showed voters favouring Britain leaving the EU by 47 percent to 44 percent.

“Our poll rather unhinges a few accepted orthodoxies,” ICM’s director Martin Boon said. “It is only one poll, but in a rather unexpected reverse of polling assumptions so far, both our phone poll and our online poll are consistent on both vote intentions and on the EU referendum.”

A poll published on Monday in The Telegraph newspaper showed support for Out rising but still behind the In campaign. Lynton Crosby, the political strategist behind Prime Minister David Cameron’s election victory, attributed the move to the focus on migration.

The ICM polls published on Tuesday were conducted between May 27 and 29. The telephone poll interviewed 1,004 people aged over 18. It found that 45 percent of respondents favoured leaving the EU compared with 42 percent who said they would vote to stay in the bloc. Thirteen percent said they did not know.

ICM interviewed 2,052 people for the online survey, which showed Out holding a three percentage point lead at 47 percent to 44 percent, and 9 percent undecided.

An online ICM poll published last week had put the two camps neck and neck at 45 percent each.