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By Elizabeth Piper LONDON (Reuters) - Thousands of refugees could flock to Britain from France if voters decide to leave the European Union, a spokesman for David Cameron said on Monday, underlining the prime minister's stance that an exit would hurt security. In what critics said was the start of a "campaign of fear" to try to keep voters in the European Union, the spokesman said leaving the bloc could harm an agreement with France which allows British border guards to make immigration checks there. "If those controls didn't continue then as we know there are thousands of people there, who are there specifically because they want to come to the UK, who would then come to the UK ... there would be nothing to stop thousands of people crossing the Channel overnight." Britain's border with France is on the French side of the Channel that separates the countries and at the northern port town of Calais, thousands of migrants are living in the so-called "Jungle" camp in the hope of crossing to England.