"More than 1,000 attempts were thwarted last night, with around 30 arrests," the source said, adding there were no reports of migrants injured in their bid to enter the undersea tunnel linking France and Britain.
Police reinforcements appeared to be having an impact, as the number of nightly attempts to penetrate the Eurotunnel premises has roughly halved since its peak at the beginning of the week.
France has sent 120 additional police officers to the northern port city of Calais to stem the crisis, as the number of deaths since June reached 10.
A spokesman for Eurotunnel said there had been "much less disruption" since the reinforcements arrived to bolster the 300-strong police contingent already stationed in the city.
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At least four coaches of riot police were today morning guarding the entrance to the tunnel, where the situation was calm.
A police source said that, while the reinforcements had helped, "the pressure of the migrants is still there" and the "situation remains difficult to deal with."
However, this source said there had been far fewer migrants managing to get onto the Eurotunnel platforms and get on the train shuttles going to England.
At least a dozen more made it past the cordon, but ran straight into a second line of officers waiting a hundred metres further down the line.
Around 3,000 people from countries including Syria and Eritrea are camping out in the northern French port of Calais and trying to cross into Britain illegally by clambering on board lorries and trains.
The crisis has become a hot political issue on both sides of the Channel and British Prime Minister David Cameron was to hold a meeting of his government's COBRA emergency committee today on the crisis.