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Former London Mayor Boris Johnson and Justice Secretary Michael Gove said Cameron, who is leading the drive for Britain to remain in the bloc, should accept that his Conservative Party's election pledge to cut annual immigration to tens of thousands has failed. The migrant flow last year increased to more than 330,000, Bloomberg wrote.

"Voters were promised repeatedly at elections that net migration could be cut to tens of thousands," Gove and Johnson wrote in the letter, published in the Sunday Times newspaper. "This promise is plainly not achievable as long as the U.K. is a member of the EU and the failure to keep it is corrosive of public trust in politics."

With less than a month to go before the June 23 referendum, the debate has turned acrimonious, with parliament's Treasury select committee on Friday accusing both sides of misleading voters with "bogus claims." After the publication of several reports by the Treasury and international organizations focused on the potential economic shock of an exit, the Leave campaign is seeking to regain control of the debate by focusing on the impact of EU membership to migration.

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'Control' Borders

"No Conservative MP who was elected at the last election can fulfill our pledge to the British people if we vote to stay in the EU," former Tory Defence Secretary and Brexit campaigner Liam Fox told the BBC's "Andrew Marr Show" on Sunday. "I want control of our own lawmaking, I want control of our own money and I want control of our own borders."

Net migration to the U.K. rose to 333,000 in 2015, just below the record, and a 20,000 increase from 2014, the Office of National Statistics said on Thursday.

Cameron remains committed to the immigration pledge. "The ambitions I've set out are the right ones," he told reporters traveling to a leaders' summit in Japan with him last week when asked if it wouldn't be easier to abandon the target.

Economists 'Remain'

"Of course the figures are disappointing," Cameron said on Friday when asked about the statistics. The high numbers are partly the result of the U.K. economy performing better than those elsewhere in Europe, he said.

Read alsoDavid Cameron: ISIS, Vladimir Putin 'might be happy' with BrexitMeanwhile, the "Remain" campaign continued to focus on the potential impact of Brexit on Britain's economy, with a poll commissioned by the Observer newspaper showing nine out of ten economists agree an exit would cause economic damage. The IPSOS Mori survey of over 600 economists showed 88 percent of respondents said leaving the EU single market would damage Britain's growth prospects over the next five years. The survey was carried out online between May 19 and May 27.

Speaking to the Marr show on Sunday, former Labour Prime Minister Tony Blair said the risks of leaving the bloc far outweighed any advantages.

"We will suffer an immediate shock to our economy, we will create years of uncertainty," Blair said. "It's an enormous economic problem. Is that pain worth the gain and what is that gain that's so important?"